|
\(\begin{matrix}
\widehat{~} x & = & (~, x) & ?
\'"`UNIQ-MathJax1-QINU`"'
In contrast, the SER for interpreter \(\text{B}\!\) yields the semiotic equations:
|
|
\([{}^{\backprime\backprime} \text{A} {}^{\prime\prime}]_\text{B}\!\)
|
\(=\!\)
|
\([{}^{\backprime\backprime} \text{u} {}^{\prime\prime}]_\text{B}\!\)
|
|
\([{}^{\backprime\backprime} \text{B} {}^{\prime\prime}]_\text{B}\!\)
|
\(=\!\)
|
\([{}^{\backprime\backprime} \text{i} {}^{\prime\prime}]_\text{B}\!\)
| | or
|
\({}^{\backprime\backprime} \text{A} {}^{\prime\prime}\!\)
|
\(=_\text{B}\!\)
|
\({}^{\backprime\backprime} \text{u} {}^{\prime\prime}\!\)
|
|
\({}^{\backprime\backprime} \text{B} {}^{\prime\prime}\!\)
|
\(=_\text{B}\!\)
|
\({}^{\backprime\backprime} \text{i} {}^{\prime\prime}\!\)
|
and the semiotic partition\[\{ \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \} , \{ {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \} \}.\!\]
6.38. Considering the Source
Attributed Sign Relation
|
\(\begin{array}{ccl}
O & = &
\{ \text{A}, \text{B} \}
\\[6pt]
S & = &
\{
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}},
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}},
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}},
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{A}},
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}},
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}},
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}},
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}
\}
\\[6pt]
I & = &
\{
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}},
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}},
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}},
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{A}},
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}},
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}},
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}},
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}
\}
\end{array}\)
|
Thus informed, the semiotic equivalence relation for interpreter \(\text{A}\!\) yields the following semiotic equations.
|
|
\([{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}]_\text{A}\!\)
|
\(=\!\)
|
\([{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}]_\text{A}\!\)
|
\(=\!\)
|
\([{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}]_\text{A}\!\)
|
\(=\!\)
|
\([{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}]_\text{A}\!\)
| | or
|
\({}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}\!\)
|
\(=_\text{A}\!\)
|
\({}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}\!\)
|
\(=_\text{A}\!\)
|
\({}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}\!\)
|
\(=_\text{A}\!\)
|
\({}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}\!\)
|
In comparison, the semiotic equivalence relation for interpreter \(\text{B}\!\) yields the following semiotic equations.
|
|
\([{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}]_\text{B}\!\)
|
\(=\!\)
|
\([{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}]_\text{B}\!\)
|
\(=\!\)
|
\([{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}]_\text{B}\!\)
|
\(=\!\)
|
\([{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}]_\text{B}\!\)
| | or
|
\({}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}\!\)
|
\(=_\text{B}\!\)
|
\({}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}\!\)
|
\(=_\text{B}\!\)
|
\({}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}\!\)
|
\(=_\text{B}\!\)
|
\({}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}\!\)
|
Consequently, the semiotic equivalence relations for \(\text{A}\!\) and \(\text{B}\!\) both induce the same semiotic partition on \(S,\!\) namely, the following.
|
\(
\{ \{
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}},
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}},
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}},
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}
\}~,~\{
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}},
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}},
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}},
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{A}}
\} \}.\!
\)
|
Augmented Sign Relation
|
\(\begin{array}{ccl}
O & = &
\{ \text{A}, \text{B} \}
\\[8pt]
S & = &
\{
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
\}
\\[8pt]
I & = &
\{
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
\}
\end{array}\)
|
|
\(\begin{array}{lll}
O & = & \{ \text{A}, \text{B} \}
\end{array}\)
|
|
\(\begin{array}{lllllll}
S
& = &
\{ &
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime},
&
\\[4pt]
& & &
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
& \}
\\[10pt]
I
& = &
\{ &
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime},
&
\\[4pt]
& & &
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
& \}
\end{array}\)
|
Relations In General
Next let's re-examine the numerical incidence properties of relations, concentrating on the definitions of the assorted regularity conditions.
For example, \(L\!\) is said to be \(^{\backprime\backprime} c\text{-regular at}~ j \, ^{\prime\prime}\) if and only if the cardinality of the local flag \(L_{x \,\text{at}\, j}\) is equal to \(c\!\) for all \(x \in X_j,\) coded in symbols, if and only if \(|L_{x \,\text{at}\, j}| = c\) for all \(x \in X_j.\)
In a similar fashion, it is possible to define the numerical incidence properties \(^{\backprime\backprime}(< c)\text{-regular at}~ j \, ^{\prime\prime},\) \(^{\backprime\backprime}(> c)\text{-regular at}~ j \, ^{\prime\prime},\) and so on. For ease of reference, a few of these definitions are recorded below.
|
\(\begin{array}{lll}
L ~\text{is}~ c\text{-regular at}~ j
& \iff &
|L_{x \,\text{at}\, j}| = c ~\text{for all}~ x \in X_j.
\\[6pt]
L ~\text{is}~ (< c)\text{-regular at}~ j
& \iff &
|L_{x \,\text{at}\, j}| < c ~\text{for all}~ x \in X_j.
\\[6pt]
L ~\text{is}~ (> c)\text{-regular at}~ j
& \iff &
|L_{x \,\text{at}\, j}| > c ~\text{for all}~ x \in X_j.
\\[6pt]
L ~\text{is}~ (\le c)\text{-regular at}~ j
& \iff &
|L_{x \,\text{at}\, j}| \le c ~\text{for all}~ x \in X_j.
\\[6pt]
L ~\text{is}~ (\ge c)\text{-regular at}~ j
& \iff &
|L_{x \,\text{at}\, j}| \ge c ~\text{for all}~ x \in X_j.
\end{array}\)
|
Clearly, if any relation is \((\le c)\text{-regular}\) on one of its domains \(X_j\!\) and also \((\ge c)\text{-regular}\) on the same domain, then it must be \((= c)\text{-regular}\!\) on that domain, in effect, \(c\text{-regular}\!\) at \(j.\!\)
Among the variety of conceivable regularities affecting 2-adic relations, we pay special attention to the \(c\!\)-regularity conditions where \(c\!\) is equal to 1.
Let \(L \subseteq X \times Y\!\) be an arbitrary 2-adic relation. The following properties of \(L\!\) can then be defined:
|
\(\begin{array}{lll}
L ~\text{is total at}~ X
& \iff &
L ~\text{is}~ (\ge 1)\text{-regular}~ \text{at}~ X.
\\[6pt]
L ~\text{is total at}~ Y
& \iff &
L ~\text{is}~ (\ge 1)\text{-regular}~ \text{at}~ Y.
\\[6pt]
L ~\text{is tubular at}~ X
& \iff &
L ~\text{is}~ (\le 1)\text{-regular}~ \text{at}~ X.
\\[6pt]
L ~\text{is tubular at}~ Y
& \iff &
L ~\text{is}~ (\le 1)\text{-regular}~ \text{at}~ Y.
\end{array}\)
|
We have already looked at 2-adic relations that separately exemplify each of these regularities. We also introduced a few bits of additional terminology and special-purpose notations for working with tubular relations.
If \(L\!\) is tubular at \(X,\!\) then \(L\!\) is known as a partial function or a prefunction from \(X\!\) to \(Y,\!\) indicated by writing \(L : X \rightharpoonup Y.\!\) We have the following definitions and notations.
|
\(\begin{array}{lll}
L ~\text{is a prefunction}~ L : X \rightharpoonup Y
& \iff &
L ~\text{is tubular at}~ X.
\\[6pt]
L ~\text{is a prefunction}~ L : X \leftharpoonup Y
& \iff &
L ~\text{is tubular at}~ Y.
\end{array}\)
|
We arrive by way of this winding stair at the special stamps of 2-adic relations \(L \subseteq X \times Y\!\) that are variously described as 1-regular, total and tubular, or total prefunctions on specified domains, either \(X\!\) or \(Y\!\) or both, and that are more often celebrated as functions on those domains.
If \(L\!\) is a prefunction \(L : X \rightharpoonup Y\!\) that happens to be total at \(X,\!\) then \(L\!\) is known as a function from \(X\!\) to \(Y,\!\) indicated by writing \(L : X \to Y.\!\) To say that a relation \(L \subseteq X \times Y\!\) is totally tubular at \(X\!\) is to say that \(L\!\) is 1-regular at \(X.\!\) Thus, we may formalize the following definitions.
|
\(\begin{array}{lll}
L ~\text{is a function}~ L : X \to Y
& \iff &
L ~\text{is}~ 1\text{-regular at}~ X.
\\[6pt]
L ~\text{is a function}~ L : X \leftarrow Y
& \iff &
L ~\text{is}~ 1\text{-regular at}~ Y.
\end{array}\)
|
In the case of a 2-adic relation \(L \subseteq X \times Y\!\) that has the qualifications of a function \(f : X \to Y,\!\) there are a number of further differentia that arise.
|
\(\begin{array}{lll}
f ~\text{is surjective}
& \iff &
f ~\text{is total at}~ Y.
\\[6pt]
f ~\text{is injective}
& \iff &
f ~\text{is tubular at}~ Y.
\\[6pt]
f ~\text{is bijective}
& \iff &
f ~\text{is}~ 1\text{-regular at}~ Y.
\end{array}\)
|
Table Work
Group Operations
\(\text{Table 32.1}~~\text{Scheme of a Group Operation Table}\)
| \(*\!\)
|
\(x_0\!\)
|
\(\cdots\!\)
|
\(x_j\!\)
|
\(\cdots\!\)
| | \(x_0\!\)
|
\(x_0 * x_0\!\)
|
\(\cdots\!\)
|
\(x_0 * x_j\!\)
|
\(\cdots\!\)
| | \(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
| | \(x_i\!\)
|
\(x_i * x_0\!\)
|
\(\cdots\!\)
|
\(x_i * x_j\!\)
|
\(\cdots\!\)
| | \(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\text{Table 32.2}~~\text{Scheme of the Regular Ante-Representation}\)
| \(\text{Element}\!\)
|
\(\text{Function as Set of Ordered Pairs of Elements}\!\)
| | \(x_0\!\)
|
\(\{\!\)
|
\((x_0 ~,~ x_0 * x_0),\!\)
|
\(\cdots\!\)
|
\((x_j ~,~ x_0 * x_j),\!\)
|
\(\cdots\!\)
|
\(\}\!\)
| | \(\cdots\!\)
|
\(\{\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\}\!\)
| | \(x_i\!\)
|
\(\{\!\)
|
\((x_0 ~,~ x_i * x_0),\!\)
|
\(\cdots\!\)
|
\((x_j ~,~ x_i * x_j),\!\)
|
\(\cdots\!\)
|
\(\}\!\)
| | \(\cdots\!\)
|
\(\{\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\}\!\)
|
\(\text{Table 32.3}~~\text{Scheme of the Regular Post-Representation}\)
| \(\text{Element}\!\)
|
\(\text{Function as Set of Ordered Pairs of Elements}\!\)
| | \(x_0\!\)
|
\(\{\!\)
|
\((x_0 ~,~ x_0 * x_0),\!\)
|
\(\cdots\!\)
|
\((x_j ~,~ x_j * x_0),\!\)
|
\(\cdots\!\)
|
\(\}\!\)
| | \(\cdots\!\)
|
\(\{\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\}\!\)
| | \(x_i\!\)
|
\(\{\!\)
|
\((x_0 ~,~ x_0 * x_i),\!\)
|
\(\cdots\!\)
|
\((x_j ~,~ x_j * x_i),\!\)
|
\(\cdots\!\)
|
\(\}\!\)
| | \(\cdots\!\)
|
\(\{\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\cdots\!\)
|
\(\}\!\)
|
\(\text{Table 33.1}~~\text{Multiplication Operation of the Group}~V_4\)
| \(\cdot\!\)
|
\(\operatorname{e}\)
|
\(\operatorname{f}\)
|
\(\operatorname{g}\)
|
\(\operatorname{h}\)
| | \(\operatorname{e}\)
|
\(\operatorname{e}\)
|
\(\operatorname{f}\)
|
\(\operatorname{g}\)
|
\(\operatorname{h}\)
| | \(\operatorname{f}\)
|
\(\operatorname{f}\)
|
\(\operatorname{e}\)
|
\(\operatorname{h}\)
|
\(\operatorname{g}\)
| | \(\operatorname{g}\)
|
\(\operatorname{g}\)
|
\(\operatorname{h}\)
|
\(\operatorname{e}\)
|
\(\operatorname{f}\)
| | \(\operatorname{h}\)
|
\(\operatorname{h}\)
|
\(\operatorname{g}\)
|
\(\operatorname{f}\)
|
\(\operatorname{e}\)
|
\(\text{Table 33.2}~~\text{Regular Representation of the Group}~V_4\)
| \(\text{Element}\!\)
|
\(\text{Function as Set of Ordered Pairs of Elements}\!\)
| | \(\operatorname{e}\)
|
\(\{\!\)
|
\((\operatorname{e}, \operatorname{e}),\)
|
\((\operatorname{f}, \operatorname{f}),\)
|
\((\operatorname{g}, \operatorname{g}),\)
|
\((\operatorname{h}, \operatorname{h})\)
|
\(\}\!\)
| | \(\operatorname{f}\)
|
\(\{\!\)
|
\((\operatorname{e}, \operatorname{f}),\)
|
\((\operatorname{f}, \operatorname{e}),\)
|
\((\operatorname{g}, \operatorname{h}),\)
|
\((\operatorname{h}, \operatorname{g})\)
|
\(\}\!\)
| | \(\operatorname{g}\)
|
\(\{\!\)
|
\((\operatorname{e}, \operatorname{g}),\)
|
\((\operatorname{f}, \operatorname{h}),\)
|
\((\operatorname{g}, \operatorname{e}),\)
|
\((\operatorname{h}, \operatorname{f})\)
|
\(\}\!\)
| | \(\operatorname{h}\)
|
\(\{\!\)
|
\((\operatorname{e}, \operatorname{h}),\)
|
\((\operatorname{f}, \operatorname{g}),\)
|
\((\operatorname{g}, \operatorname{f}),\)
|
\((\operatorname{h}, \operatorname{e})\)
|
\(\}\!\)
|
\(\text{Table 33.3}~~\text{Regular Representation of the Group}~V_4\)
| \(\text{Element}\!\)
|
\(\text{Function as Set of Ordered Pairs of Symbols}\!\)
| | \(\operatorname{e}\)
|
\(\{\!\)
|
\(({}^{\backprime\backprime}\text{e}{}^{\prime\prime}, {}^{\backprime\backprime}\text{e}{}^{\prime\prime}),\)
|
\(({}^{\backprime\backprime}\text{f}{}^{\prime\prime}, {}^{\backprime\backprime}\text{f}{}^{\prime\prime}),\)
|
\(({}^{\backprime\backprime}\text{g}{}^{\prime\prime}, {}^{\backprime\backprime}\text{g}{}^{\prime\prime}),\)
|
\(({}^{\backprime\backprime}\text{h}{}^{\prime\prime}, {}^{\backprime\backprime}\text{h}{}^{\prime\prime})\)
|
\(\}\!\)
| | \(\operatorname{f}\)
|
\(\{\!\)
|
\(({}^{\backprime\backprime}\text{e}{}^{\prime\prime}, {}^{\backprime\backprime}\text{f}{}^{\prime\prime}),\)
|
\(({}^{\backprime\backprime}\text{f}{}^{\prime\prime}, {}^{\backprime\backprime}\text{e}{}^{\prime\prime}),\)
|
\(({}^{\backprime\backprime}\text{g}{}^{\prime\prime}, {}^{\backprime\backprime}\text{h}{}^{\prime\prime}),\)
|
\(({}^{\backprime\backprime}\text{h}{}^{\prime\prime}, {}^{\backprime\backprime}\text{g}{}^{\prime\prime})\)
|
\(\}\!\)
| | \(\operatorname{g}\)
|
\(\{\!\)
|
\(({}^{\backprime\backprime}\text{e}{}^{\prime\prime}, {}^{\backprime\backprime}\text{g}{}^{\prime\prime}),\)
|
\(({}^{\backprime\backprime}\text{f}{}^{\prime\prime}, {}^{\backprime\backprime}\text{h}{}^{\prime\prime}),\)
|
\(({}^{\backprime\backprime}\text{g}{}^{\prime\prime}, {}^{\backprime\backprime}\text{e}{}^{\prime\prime}),\)
|
\(({}^{\backprime\backprime}\text{h}{}^{\prime\prime}, {}^{\backprime\backprime}\text{f}{}^{\prime\prime})\)
|
\(\}\!\)
| | \(\operatorname{h}\)
|
\(\{\!\)
|
\(({}^{\backprime\backprime}\text{e}{}^{\prime\prime}, {}^{\backprime\backprime}\text{h}{}^{\prime\prime}),\)
|
\(({}^{\backprime\backprime}\text{f}{}^{\prime\prime}, {}^{\backprime\backprime}\text{g}{}^{\prime\prime}),\)
|
\(({}^{\backprime\backprime}\text{g}{}^{\prime\prime}, {}^{\backprime\backprime}\text{f}{}^{\prime\prime}),\)
|
\(({}^{\backprime\backprime}\text{h}{}^{\prime\prime}, {}^{\backprime\backprime}\text{e}{}^{\prime\prime})\)
|
\(\}\!\)
|
\(\text{Table 34.1}~~\text{Multiplicative Presentation of the Group}~Z_4(\cdot)\)
| \(\cdot\!\)
|
\(\operatorname{1}\)
|
\(\operatorname{a}\)
|
\(\operatorname{b}\)
|
\(\operatorname{c}\)
| | \(\operatorname{1}\)
|
\(\operatorname{1}\)
|
\(\operatorname{a}\)
|
\(\operatorname{b}\)
|
\(\operatorname{c}\)
| | \(\operatorname{a}\)
|
\(\operatorname{a}\)
|
\(\operatorname{b}\)
|
\(\operatorname{c}\)
|
\(\operatorname{1}\)
| | \(\operatorname{b}\)
|
\(\operatorname{b}\)
|
\(\operatorname{c}\)
|
\(\operatorname{1}\)
|
\(\operatorname{a}\)
| | \(\operatorname{c}\)
|
\(\operatorname{c}\)
|
\(\operatorname{1}\)
|
\(\operatorname{a}\)
|
\(\operatorname{b}\)
|
\(\text{Table 34.2}~~\text{Regular Representation of the Group}~Z_4(\cdot)\)
| \(\text{Element}\!\)
|
\(\text{Function as Set of Ordered Pairs of Elements}\!\)
| | \(\operatorname{1}\)
|
\(\{\!\)
|
\((\operatorname{1}, \operatorname{1}),\)
|
\((\operatorname{a}, \operatorname{a}),\)
|
\((\operatorname{b}, \operatorname{b}),\)
|
\((\operatorname{c}, \operatorname{c})\)
|
\(\}\!\)
| | \(\operatorname{a}\)
|
\(\{\!\)
|
\((\operatorname{1}, \operatorname{a}),\)
|
\((\operatorname{a}, \operatorname{b}),\)
|
\((\operatorname{b}, \operatorname{c}),\)
|
\((\operatorname{c}, \operatorname{1})\)
|
\(\}\!\)
| | \(\operatorname{b}\)
|
\(\{\!\)
|
\((\operatorname{1}, \operatorname{b}),\)
|
\((\operatorname{a}, \operatorname{c}),\)
|
\((\operatorname{b}, \operatorname{1}),\)
|
\((\operatorname{c}, \operatorname{a})\)
|
\(\}\!\)
| | \(\operatorname{c}\)
|
\(\{\!\)
|
\((\operatorname{1}, \operatorname{c}),\)
|
\((\operatorname{a}, \operatorname{1}),\)
|
\((\operatorname{b}, \operatorname{a}),\)
|
\((\operatorname{c}, \operatorname{b})\)
|
\(\}\!\)
|
\(\text{Table 35.1}~~\text{Additive Presentation of the Group}~Z_4(+)\)
| \(+\!\)
|
\(\operatorname{0}\)
|
\(\operatorname{1}\)
|
\(\operatorname{2}\)
|
\(\operatorname{3}\)
| | \(\operatorname{0}\)
|
\(\operatorname{0}\)
|
\(\operatorname{1}\)
|
\(\operatorname{2}\)
|
\(\operatorname{3}\)
| | \(\operatorname{1}\)
|
\(\operatorname{1}\)
|
\(\operatorname{2}\)
|
\(\operatorname{3}\)
|
\(\operatorname{0}\)
| | \(\operatorname{2}\)
|
\(\operatorname{2}\)
|
\(\operatorname{3}\)
|
\(\operatorname{0}\)
|
\(\operatorname{1}\)
| | \(\operatorname{3}\)
|
\(\operatorname{3}\)
|
\(\operatorname{0}\)
|
\(\operatorname{1}\)
|
\(\operatorname{2}\)
|
\(\text{Table 35.2}~~\text{Regular Representation of the Group}~Z_4(+)\)
| \(\text{Element}\!\)
|
\(\text{Function as Set of Ordered Pairs of Elements}\!\)
| | \(\operatorname{0}\)
|
\(\{\!\)
|
\((\operatorname{0}, \operatorname{0}),\)
|
\((\operatorname{1}, \operatorname{1}),\)
|
\((\operatorname{2}, \operatorname{2}),\)
|
\((\operatorname{3}, \operatorname{3})\)
|
\(\}\!\)
| | \(\operatorname{1}\)
|
\(\{\!\)
|
\((\operatorname{0}, \operatorname{1}),\)
|
\((\operatorname{1}, \operatorname{2}),\)
|
\((\operatorname{2}, \operatorname{3}),\)
|
\((\operatorname{3}, \operatorname{0})\)
|
\(\}\!\)
| | \(\operatorname{2}\)
|
\(\{\!\)
|
\((\operatorname{0}, \operatorname{2}),\)
|
\((\operatorname{1}, \operatorname{3}),\)
|
\((\operatorname{2}, \operatorname{0}),\)
|
\((\operatorname{3}, \operatorname{1})\)
|
\(\}\!\)
| | \(\operatorname{3}\)
|
\(\{\!\)
|
\((\operatorname{0}, \operatorname{3}),\)
|
\((\operatorname{1}, \operatorname{0}),\)
|
\((\operatorname{2}, \operatorname{1}),\)
|
\((\operatorname{3}, \operatorname{2})\)
|
\(\}\!\)
|
Sign Relations
\(\text{Table 1.} ~~ \text{Sign Relation of Interpreter A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\text{Table 2.} ~~ \text{Sign Relation of Interpreter B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\text{Table 36.} ~~ \text{Semantics for Higher Order Signs}\!\)
| \(\text{Object Denoted}\!\)
|
\(\text{Equivalent Signs}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
& = &
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\langle} \text{B} {}^{\rangle}
& = &
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
& = &
{}^{\langle\backprime\backprime} \text{A} {}^{\prime\prime\rangle}
& = &
{}^{\backprime\backprime\langle} \text{A} {}^{\rangle\prime\prime}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
& = &
{}^{\langle\backprime\backprime} \text{B} {}^{\prime\prime\rangle}
& = &
{}^{\backprime\backprime\langle} \text{B} {}^{\rangle\prime\prime}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
& = &
{}^{\langle\backprime\backprime} \text{i} {}^{\prime\prime\rangle}
& = &
{}^{\backprime\backprime\langle} \text{i} {}^{\rangle\prime\prime}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
& = &
{}^{\langle\backprime\backprime} \text{u} {}^{\prime\prime\rangle}
& = &
{}^{\backprime\backprime\langle} \text{u} {}^{\rangle\prime\prime}
\end{matrix}\)
|
\(\text{Table 37.} ~~ \text{Sign Relation Containing a Higher Order Sign}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\ldots
\\[2pt]
\ldots
\\[2pt]
\text{s}
\end{matrix}\)
|
\(\begin{matrix}
\text{s}
\\[2pt]
\ldots
\\[2pt]
\text{t}
\end{matrix}\)
|
\(\begin{matrix}
\ldots
\\[2pt]
\ldots
\\[2pt]
\ldots
\end{matrix}\)
|
\(\text{Table 38.} ~~ \text{Sign Relation for a Succession of Higher Order Signs (1)}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
x
\\[2pt]
{}^{\langle} x {}^{\rangle}
\\[2pt]
{}^{\langle\langle} x {}^{\rangle\rangle}
\\[2pt]
\ldots
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} x {}^{\rangle}
\\[2pt]
{}^{\langle\langle} x {}^{\rangle\rangle}
\\[2pt]
{}^{\langle\langle\langle} x {}^{\rangle\rangle\rangle}
\\[2pt]
\ldots
\end{matrix}\)
|
\(\begin{matrix}
\ldots
\\[2pt]
\ldots
\\[2pt]
\ldots
\\[2pt]
\ldots
\end{matrix}\)
|
\(\text{Table 39.} ~~ \text{Sign Relation for a Succession of Higher Order Signs (2)}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
x
\\[2pt]
s_1
\\[2pt]
s_2
\\[2pt]
\ldots
\end{matrix}\)
|
\(\begin{matrix}
s_1
\\[2pt]
s_2
\\[2pt]
s_3
\\[2pt]
\ldots
\end{matrix}\)
|
\(\begin{matrix}
\ldots
\\[2pt]
\ldots
\\[2pt]
\ldots
\\[2pt]
\ldots
\end{matrix}\)
|
\(\text{Table 40.} ~~ \text{Reflective Origin} ~ \operatorname{Ref}^0 L(\text{A})\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 41.} ~~ \text{Reflective Origin} ~ \operatorname{Ref}^0 L(\text{B})\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 42.} ~~ \text{Higher Ascent Sign Relation} ~ \operatorname{Ref}^1 L(\text{A})\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
\end{matrix}\)
|
\(\text{Table 43.} ~~ \text{Higher Ascent Sign Relation} ~ \operatorname{Ref}^1 L(\text{B})\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
\end{matrix}\)
|
\(\text{Table 44.} ~~ \text{Higher Import Sign Relation} ~ \operatorname{HI}^1 L(\text{A})\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 45.} ~~ \text{Higher Import Sign Relation} ~ \operatorname{HI}^1 L(\text{B})\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 46.} ~~ \text{Higher Order Sign Relation for} ~ Q(\text{A}, \text{B})\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} L {}^{\rangle}
\\
{}^{\langle} L {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} L {}^{\rangle}
\\
{}^{\langle} L {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} q {}^{\rangle}
\\
{}^{\langle} q {}^{\rangle}
\\
{}^{\langle} q {}^{\rangle}
\\
{}^{\langle} q {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} q {}^{\rangle}
\\
{}^{\langle} q {}^{\rangle}
\\
{}^{\langle} q {}^{\rangle}
\\
{}^{\langle} q {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
\\
( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
\\
( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
(( & {}^{\langle} \text{A} {}^{\rangle} & , & \text{A} & ), & \text{A} & )
\\
(( & {}^{\langle} \text{A} {}^{\rangle} & , & \text{B} & ), & \text{A} & )
\\
(( & {}^{\langle} \text{B} {}^{\rangle} & , & \text{A} & ), & \text{B} & )
\\
(( & {}^{\langle} \text{B} {}^{\rangle} & , & \text{B} & ), & \text{B} & )
\\
(( & {}^{\langle} \text{i} {}^{\rangle} & , & \text{A} & ), & \text{A} & )
\\
(( & {}^{\langle} \text{i} {}^{\rangle} & , & \text{B} & ), & \text{B} & )
\\
(( & {}^{\langle} \text{u} {}^{\rangle} & , & \text{A} & ), & \text{B} & )
\\
(( & {}^{\langle} \text{u} {}^{\rangle} & , & \text{B} & ), & \text{A} & )
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\\
{}^{\langle} \operatorname{De} {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 48.1} ~~ \operatorname{ER}(L_\text{A}) : \text{Extensional Representation of} ~ L_\text{A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 48.2} ~~ \operatorname{ER}(\operatorname{Den}(L_\text{A})) : \text{Denotative Component of} ~ L_\text{A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
({}^{\langle} \text{A} {}^{\rangle}, \text{A})
\\
({}^{\langle} \text{i} {}^{\rangle}, \text{A})
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
({}^{\langle} \text{B} {}^{\rangle}, \text{B})
\\
({}^{\langle} \text{u} {}^{\rangle}, \text{B})
\end{matrix}\)
|
\(\text{Table 48.3} ~~ \operatorname{ER}(\operatorname{Con}(L_\text{A})) : \text{Connotative Component of} ~ L_\text{A}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
({}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{A} {}^{\rangle})
\\
({}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle})
\\
({}^{\langle} \text{i} {}^{\rangle}, {}^{\langle} \text{A} {}^{\rangle})
\\
({}^{\langle} \text{i} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle})
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
({}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{B} {}^{\rangle})
\\
({}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle})
\\
({}^{\langle} \text{u} {}^{\rangle}, {}^{\langle} \text{B} {}^{\rangle})
\\
({}^{\langle} \text{u} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle})
\end{matrix}\)
|
\(\text{Table 49.1} ~~ \operatorname{ER}(L_\text{B}) : \text{Extensional Representation of} ~ L_\text{B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 49.2} ~~ \operatorname{ER}(\operatorname{Den}(L_\text{B})) : \text{Denotative Component of} ~ L_\text{B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
({}^{\langle} \text{A} {}^{\rangle}, \text{A})
\\
({}^{\langle} \text{u} {}^{\rangle}, \text{A})
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
({}^{\langle} \text{B} {}^{\rangle}, \text{B})
\\
({}^{\langle} \text{i} {}^{\rangle}, \text{B})
\end{matrix}\)
|
\(\text{Table 49.3} ~~ \operatorname{ER}(\operatorname{Con}(L_\text{B})) : \text{Connotative Component of} ~ L_\text{B}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
({}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{A} {}^{\rangle})
\\
({}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle})
\\
({}^{\langle} \text{u} {}^{\rangle}, {}^{\langle} \text{A} {}^{\rangle})
\\
({}^{\langle} \text{u} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle})
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
({}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{B} {}^{\rangle})
\\
({}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle})
\\
({}^{\langle} \text{i} {}^{\rangle}, {}^{\langle} \text{B} {}^{\rangle})
\\
({}^{\langle} \text{i} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle})
\end{matrix}\)
|
Sign Processes
Blocked Version
\(\text{Table 78.} ~~ \text{Sign Process of Interpreter A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\text{Table 79.} ~~ \text{Sign Process of Interpreter B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
Sorted Version
\(\text{Table 78.} ~~ \text{Sign Process of Interpreter A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\text{Table 79.} ~~ \text{Sign Process of Interpreter B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
Type Tables
\(\text{Table 47.1} ~~ \text{Basic Types for ERs and IRs of Sign Relations}\!\)
| \(\text{Type}\!\) |
\(\text{Symbol}\!\)
| |
\(\begin{array}{l}
\text{Property} \\ \text{Sign} \\ \text{Set} \\ \text{Triple}\\ \text{Underlying Element}
\end{array}\)
|
\(\begin{matrix}
P \\ \underline{S} \\ S \\ T \\ U
\end{matrix}\)
|
\(\text{Table 47.2} ~~ \text{Derived Types for ERs of Sign Relations}\!\)
| \(\text{Type}\!\)
|
\(\text{Symbol}\!\)
|
\(\text{Construction}\!\)
| | \(\text{Relation}\!\)
|
\(R\!\)
|
\(S(T(U))\!\)
|
\(\text{Table 47.3} ~~ \text{Derived Types for IRs of Sign Relations}\!\)
| \(\text{Type}\!\)
|
\(\text{Symbol}\!\)
|
\(\text{Construction}\!\)
| | \(\text{Relation}\!\)
|
\(P(R)\!\)
|
\(P(S(T(U)))\!\)
|
Completed Work
\(\text{Table 50.} ~~ \text{Notations for Objects and Their Signs}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign of Object}\!\)
| |
\(\begin{matrix}
\text{A} &
\text{A} &
w_1
\\[6pt]
\text{B} &
\text{B} &
w_2
\\[12pt]
{}^{\backprime\backprime} \text{A} {}^{\prime\prime} &
{}^{\langle} \text{A} {}^{\rangle} &
w_3
\\[6pt]
{}^{\backprime\backprime} \text{B} {}^{\prime\prime} &
{}^{\langle} \text{B} {}^{\rangle} &
w_4
\\[6pt]
{}^{\backprime\backprime} \text{i} {}^{\prime\prime} &
{}^{\langle} \text{i} {}^{\rangle} &
w_5
\\[6pt]
{}^{\backprime\backprime} \text{u} {}^{\prime\prime} &
{}^{\langle} \text{u} {}^{\rangle} &
w_6
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle} &
{}^{\langle} \text{A} {}^{\rangle} &
{}^{\langle} w_1 {}^{\rangle}
\\[6pt]
{}^{\langle} \text{B} {}^{\rangle} &
{}^{\langle} \text{B} {}^{\rangle} &
{}^{\langle} w_2 {}^{\rangle}
\\[12pt]
{}^{\langle\backprime\backprime} \text{A} {}^{\prime\prime\rangle} &
{}^{\langle\langle} \text{A} {}^{\rangle\rangle} &
{}^{\langle} w_3 {}^{\rangle}
\\[6pt]
{}^{\langle\backprime\backprime} \text{B} {}^{\prime\prime\rangle} &
{}^{\langle\langle} \text{B} {}^{\rangle\rangle} &
{}^{\langle} w_4 {}^{\rangle}
\\[6pt]
{}^{\langle\backprime\backprime} \text{i} {}^{\prime\prime\rangle} &
{}^{\langle\langle} \text{i} {}^{\rangle\rangle} &
{}^{\langle} w_5 {}^{\rangle}
\\[6pt]
{}^{\langle\backprime\backprime} \text{u} {}^{\prime\prime\rangle} &
{}^{\langle\langle} \text{u} {}^{\rangle\rangle} &
{}^{\langle} w_6 {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 51.1} ~~ \text{Notations for Properties and Their Signs (1)}\!\)
| \(\text{Property}\!\)
|
\(\text{Sign of Property}\!\)
| |
\(\begin{matrix}
{}^{\lbrace} \text{A} {}^{\rbrace} &
{}^{\lbrace} \text{A} {}^{\rbrace} &
{}^{\lbrace} w_1 {}^{\rbrace}
\\[6pt]
{}^{\lbrace} \text{B} {}^{\rbrace} &
{}^{\lbrace} \text{B} {}^{\rbrace} &
{}^{\lbrace} w_2 {}^{\rbrace}
\\[12pt]
{}^{\lbrace\backprime\backprime} \text{A} {}^{\prime\prime\rbrace} &
{}^{\lbrace\langle} \text{A} {}^{\rangle\rbrace} &
{}^{\lbrace} w_3 {}^{\rbrace}
\\[6pt]
{}^{\lbrace\backprime\backprime} \text{B} {}^{\prime\prime\rbrace} &
{}^{\lbrace\langle} \text{B} {}^{\rangle\rbrace} &
{}^{\lbrace} w_4 {}^{\rbrace}
\\[6pt]
{}^{\lbrace\backprime\backprime} \text{i} {}^{\prime\prime\rbrace} &
{}^{\lbrace\langle} \text{i} {}^{\rangle\rbrace} &
{}^{\lbrace} w_5 {}^{\rbrace}
\\[6pt]
{}^{\lbrace\backprime\backprime} \text{u} {}^{\prime\prime\rbrace} &
{}^{\lbrace\langle} \text{u} {}^{\rangle\rbrace} &
{}^{\lbrace} w_6 {}^{\rbrace}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle\lbrace} \text{A} {}^{\rbrace\rangle} &
{}^{\langle\lbrace} \text{A} {}^{\rbrace\rangle} &
{}^{\langle\lbrace} w_1 {}^{\rbrace\rangle}
\\[6pt]
{}^{\langle\lbrace} \text{B} {}^{\rbrace\rangle} &
{}^{\langle\lbrace} \text{B} {}^{\rbrace\rangle} &
{}^{\langle\lbrace} w_2 {}^{\rbrace\rangle}
\\[12pt]
{}^{\langle\lbrace\backprime\backprime} \text{A} {}^{\prime\prime\rbrace\rangle} &
{}^{\langle\lbrace\langle} \text{A} {}^{\rangle\rbrace\rangle} &
{}^{\langle\lbrace} w_3 {}^{\rbrace\rangle}
\\[6pt]
{}^{\langle\lbrace\backprime\backprime} \text{B} {}^{\prime\prime\rbrace\rangle} &
{}^{\langle\lbrace\langle} \text{B} {}^{\rangle\rbrace\rangle} &
{}^{\langle\lbrace} w_4 {}^{\rbrace\rangle}
\\[6pt]
{}^{\langle\lbrace\backprime\backprime} \text{i} {}^{\prime\prime\rbrace\rangle} &
{}^{\langle\lbrace\langle} \text{i} {}^{\rangle\rbrace\rangle} &
{}^{\langle\lbrace} w_5 {}^{\rbrace\rangle}
\\[6pt]
{}^{\langle\lbrace\backprime\backprime} \text{u} {}^{\prime\prime\rbrace\rangle} &
{}^{\langle\lbrace\langle} \text{u} {}^{\rangle\rbrace\rangle} &
{}^{\langle\lbrace} w_6 {}^{\rbrace\rangle}
\end{matrix}\)
|
\(\text{Table 51.2} ~~ \text{Notations for Properties and Their Signs (2)}\!\)
| \(\text{Property}\!\)
|
\(\text{Sign of Property}\!\)
| |
\(\begin{matrix}
\underline{\underline{\text{A}}} &
\underline{\underline{\text{A}}} &
\underline{\underline{w_1}}
\\[6pt]
\underline{\underline{\text{B}}} &
\underline{\underline{\text{B}}} &
\underline{\underline{w_2}}
\\[12pt]
\underline{\underline{{}^{\backprime\backprime} \text{A} {}^{\prime\prime}}} &
\underline{\underline{{}^{\langle} \text{A} {}^{\rangle}}} &
\underline{\underline{w_3}}
\\[6pt]
\underline{\underline{{}^{\backprime\backprime} \text{B} {}^{\prime\prime}}} &
\underline{\underline{{}^{\langle} \text{B} {}^{\rangle}}} &
\underline{\underline{w_4}}
\\[6pt]
\underline{\underline{{}^{\backprime\backprime} \text{i} {}^{\prime\prime}}} &
\underline{\underline{{}^{\langle} \text{i} {}^{\rangle}}} &
\underline{\underline{w_5}}
\\[6pt]
\underline{\underline{{}^{\backprime\backprime} \text{u} {}^{\prime\prime}}} &
\underline{\underline{{}^{\langle} \text{u} {}^{\rangle}}} &
\underline{\underline{w_6}}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \underline{\underline{\text{A}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{\text{A}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{w_1}} {}^{\rangle}
\\[6pt]
{}^{\langle} \underline{\underline{\text{B}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{\text{B}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{w_2}} {}^{\rangle}
\\[12pt]
{}^{\langle} \underline{\underline{{}^{\backprime\backprime} \text{A} {}^{\prime\prime}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{{}^{\langle} \text{A} {}^{\rangle}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{w_3}} {}^{\rangle}
\\[6pt]
{}^{\langle} \underline{\underline{{}^{\backprime\backprime} \text{B} {}^{\prime\prime}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{{}^{\langle} \text{B} {}^{\rangle}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{w_4}} {}^{\rangle}
\\[6pt]
{}^{\langle} \underline{\underline{{}^{\backprime\backprime} \text{i} {}^{\prime\prime}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{{}^{\langle} \text{i} {}^{\rangle}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{w_5}} {}^{\rangle}
\\[6pt]
{}^{\langle} \underline{\underline{{}^{\backprime\backprime} \text{u} {}^{\prime\prime}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{{}^{\langle} \text{u} {}^{\rangle}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{w_6}} {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 51.3} ~~ \text{Notations for Properties and Their Signs (3)}\!\)
| \(\text{Property}\!\)
|
\(\text{Sign of Property}\!\)
| |
\(\begin{matrix}
\underline{\underline{\text{A}}} &
\underline{\underline{o_1}} &
\underline{\underline{w_1}}
\\[6pt]
\underline{\underline{\text{B}}} &
\underline{\underline{o_2}} &
\underline{\underline{w_2}}
\\[12pt]
\underline{\underline{\text{a}}} &
\underline{\underline{s_1}} &
\underline{\underline{w_3}}
\\[6pt]
\underline{\underline{\text{b}}} &
\underline{\underline{s_2}} &
\underline{\underline{w_4}}
\\[6pt]
\underline{\underline{\text{i}}} &
\underline{\underline{s_3}} &
\underline{\underline{w_5}}
\\[6pt]
\underline{\underline{\text{u}}} &
\underline{\underline{s_4}} &
\underline{\underline{w_6}}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \underline{\underline{\text{A}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{o_1}} {}^{\rangle} &
{}^{\langle} \underline{\underline{w_1}} {}^{\rangle}
\\[6pt]
{}^{\langle} \underline{\underline{\text{B}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{o_2}} {}^{\rangle} &
{}^{\langle} \underline{\underline{w_2}} {}^{\rangle}
\\[12pt]
{}^{\langle} \underline{\underline{\text{a}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{s_1}} {}^{\rangle} &
{}^{\langle} \underline{\underline{w_3}} {}^{\rangle}
\\[6pt]
{}^{\langle} \underline{\underline{\text{b}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{s_2}} {}^{\rangle} &
{}^{\langle} \underline{\underline{w_4}} {}^{\rangle}
\\[6pt]
{}^{\langle} \underline{\underline{\text{i}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{s_3}} {}^{\rangle} &
{}^{\langle} \underline{\underline{w_5}} {}^{\rangle}
\\[6pt]
{}^{\langle} \underline{\underline{\text{u}}} {}^{\rangle} &
{}^{\langle} \underline{\underline{s_4}} {}^{\rangle} &
{}^{\langle} \underline{\underline{w_6}} {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 52.1} ~~ \text{Notations for Instances and Their Signs (1)}\!\)
| \(\text{Instance}\!\)
|
\(\text{Sign of Instance}\!\)
| |
\(\begin{matrix}
{}^{\lbrack} \text{A} {}^{\rbrack} &
{}^{\lbrack} \text{A} {}^{\rbrack} &
{}^{\lbrack} w_1 {}^{\rbrack}
\\[6pt]
{}^{\lbrack} \text{B} {}^{\rbrack} &
{}^{\lbrack} \text{B} {}^{\rbrack} &
{}^{\lbrack} w_2 {}^{\rbrack}
\\[12pt]
{}^{\lbrack\backprime\backprime} \text{A} {}^{\prime\prime\rbrack} &
{}^{\lbrack\langle} \text{A} {}^{\rangle\rbrack} &
{}^{\lbrack} w_3 {}^{\rbrack}
\\[6pt]
{}^{\lbrack\backprime\backprime} \text{B} {}^{\prime\prime\rbrack} &
{}^{\lbrack\langle} \text{B} {}^{\rangle\rbrack} &
{}^{\lbrack} w_4 {}^{\rbrack}
\\[6pt]
{}^{\lbrack\backprime\backprime} \text{i} {}^{\prime\prime\rbrack} &
{}^{\lbrack\langle} \text{i} {}^{\rangle\rbrack} &
{}^{\lbrack} w_5 {}^{\rbrack}
\\[6pt]
{}^{\lbrack\backprime\backprime} \text{u} {}^{\prime\prime\rbrack} &
{}^{\lbrack\langle} \text{u} {}^{\rangle\rbrack} &
{}^{\lbrack} w_6 {}^{\rbrack}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle\lbrack} \text{A} {}^{\rbrack\rangle} &
{}^{\langle\lbrack} \text{A} {}^{\rbrack\rangle} &
{}^{\langle\lbrack} w_1 {}^{\rbrack\rangle}
\\[6pt]
{}^{\langle\lbrack} \text{B} {}^{\rbrack\rangle} &
{}^{\langle\lbrack} \text{B} {}^{\rbrack\rangle} &
{}^{\langle\lbrack} w_2 {}^{\rbrack\rangle}
\\[12pt]
{}^{\langle\lbrack\backprime\backprime} \text{A} {}^{\prime\prime\rbrack\rangle} &
{}^{\langle\lbrack\langle} \text{A} {}^{\rangle\rbrack\rangle} &
{}^{\langle\lbrack} w_3 {}^{\rbrack\rangle}
\\[6pt]
{}^{\langle\lbrack\backprime\backprime} \text{B} {}^{\prime\prime\rbrack\rangle} &
{}^{\langle\lbrack\langle} \text{B} {}^{\rangle\rbrack\rangle} &
{}^{\langle\lbrack} w_4 {}^{\rbrack\rangle}
\\[6pt]
{}^{\langle\lbrack\backprime\backprime} \text{i} {}^{\prime\prime\rbrack\rangle} &
{}^{\langle\lbrack\langle} \text{i} {}^{\rangle\rbrack\rangle} &
{}^{\langle\lbrack} w_5 {}^{\rbrack\rangle}
\\[6pt]
{}^{\langle\lbrack\backprime\backprime} \text{u} {}^{\prime\prime\rbrack\rangle} &
{}^{\langle\lbrack\langle} \text{u} {}^{\rangle\rbrack\rangle} &
{}^{\langle\lbrack} w_6 {}^{\rbrack\rangle}
\end{matrix}\)
|
\(\text{Table 52.2} ~~ \text{Notations for Instances and Their Signs (2)}\!\)
| \(\text{Instance}\!\)
|
\(\text{Sign of Instance}\!\)
| |
\(\begin{matrix}
\overline{\text{A}} &
\overline{\text{A}} &
\overline{w_1}
\\[6pt]
\overline{\text{B}} &
\overline{\text{B}} &
\overline{w_2}
\\[12pt]
\overline{{}^{\backprime\backprime} \text{A} {}^{\prime\prime}} &
\overline{{}^{\langle} \text{A} {}^{\rangle}} &
\overline{w_3}
\\[6pt]
\overline{{}^{\backprime\backprime} \text{B} {}^{\prime\prime}} &
\overline{{}^{\langle} \text{B} {}^{\rangle}} &
\overline{w_4}
\\[6pt]
\overline{{}^{\backprime\backprime} \text{i} {}^{\prime\prime}} &
\overline{{}^{\langle} \text{i} {}^{\rangle}} &
\overline{w_5}
\\[6pt]
\overline{{}^{\backprime\backprime} \text{u} {}^{\prime\prime}} &
\overline{{}^{\langle} \text{u} {}^{\rangle}} &
\overline{w_6}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \overline{\text{A}} {}^{\rangle} &
{}^{\langle} \overline{\text{A}} {}^{\rangle} &
{}^{\langle} \overline{w_1} {}^{\rangle}
\\[6pt]
{}^{\langle} \overline{\text{B}} {}^{\rangle} &
{}^{\langle} \overline{\text{B}} {}^{\rangle} &
{}^{\langle} \overline{w_2} {}^{\rangle}
\\[12pt]
{}^{\langle} \overline{{}^{\backprime\backprime} \text{A} {}^{\prime\prime}} {}^{\rangle} &
{}^{\langle} \overline{{}^{\langle} \text{A} {}^{\rangle}} {}^{\rangle} &
{}^{\langle} \overline{w_3} {}^{\rangle}
\\[6pt]
{}^{\langle} \overline{{}^{\backprime\backprime} \text{B} {}^{\prime\prime}} {}^{\rangle} &
{}^{\langle} \overline{{}^{\langle} \text{B} {}^{\rangle}} {}^{\rangle} &
{}^{\langle} \overline{w_4} {}^{\rangle}
\\[6pt]
{}^{\langle} \overline{{}^{\backprime\backprime} \text{i} {}^{\prime\prime}} {}^{\rangle} &
{}^{\langle} \overline{{}^{\langle} \text{i} {}^{\rangle}} {}^{\rangle} &
{}^{\langle} \overline{w_5} {}^{\rangle}
\\[6pt]
{}^{\langle} \overline{{}^{\backprime\backprime} \text{u} {}^{\prime\prime}} {}^{\rangle} &
{}^{\langle} \overline{{}^{\langle} \text{u} {}^{\rangle}} {}^{\rangle} &
{}^{\langle} \overline{w_6} {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 52.3} ~~ \text{Notations for Instances and Their Signs (3)}\!\)
| \(\text{Instance}\!\)
|
\(\text{Sign of Instance}\!\)
| |
\(\begin{matrix}
\overline{\text{A}} &
\overline{o_1} &
\overline{w_1}
\\[6pt]
\overline{\text{B}} &
\overline{o_2} &
\overline{w_2}
\\[12pt]
\overline{\text{a}} &
\overline{s_1} &
\overline{w_3}
\\[6pt]
\overline{\text{b}} &
\overline{s_2} &
\overline{w_4}
\\[6pt]
\overline{\text{i}} &
\overline{s_3} &
\overline{w_5}
\\[6pt]
\overline{\text{u}} &
\overline{s_4} &
\overline{w_6}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \overline{\text{A}} {}^{\rangle} &
{}^{\langle} \overline{o_1} {}^{\rangle} &
{}^{\langle} \overline{w_1} {}^{\rangle}
\\[6pt]
{}^{\langle} \overline{\text{B}} {}^{\rangle} &
{}^{\langle} \overline{o_2} {}^{\rangle} &
{}^{\langle} \overline{w_2} {}^{\rangle}
\\[12pt]
{}^{\langle} \overline{\text{a}} {}^{\rangle} &
{}^{\langle} \overline{s_1} {}^{\rangle} &
{}^{\langle} \overline{w_3} {}^{\rangle}
\\[6pt]
{}^{\langle} \overline{\text{b}} {}^{\rangle} &
{}^{\langle} \overline{s_2} {}^{\rangle} &
{}^{\langle} \overline{w_4} {}^{\rangle}
\\[6pt]
{}^{\langle} \overline{\text{i}} {}^{\rangle} &
{}^{\langle} \overline{s_3} {}^{\rangle} &
{}^{\langle} \overline{w_5} {}^{\rangle}
\\[6pt]
{}^{\langle} \overline{\text{u}} {}^{\rangle} &
{}^{\langle} \overline{s_4} {}^{\rangle} &
{}^{\langle} \overline{w_6} {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 53.1} ~~ \text{Elements of} ~ \operatorname{ER}(W)\!\)
\(\text{Mnemonic Element}\!\)
\(w \in W\!\)
|
\(\text{Pragmatic Element}\!\)
\(w \in W\!\)
|
\(\text{Abstract Element}\!\)
\(w_i \in W\!\)
| |
\(\begin{matrix}
\text{A}
\\[4pt]
\text{B}
\\[4pt]
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
o_1
\\[4pt]
o_2
\\[4pt]
s_1
\\[4pt]
s_2
\\[4pt]
s_3
\\[4pt]
s_4
\end{matrix}\)
|
\(\begin{matrix}
w_1
\\[4pt]
w_2
\\[4pt]
w_3
\\[4pt]
w_4
\\[4pt]
w_5
\\[4pt]
w_6
\end{matrix}\)
|
\(\text{Table 53.2} ~~ \text{Features of} ~ \operatorname{LIR}(W)\!\)
|
\(\text{Mnemonic Feature}\!\)
\(\underline{\underline{w}} \in \underline{\underline{W}}\!\)
|
\(\text{Pragmatic Feature}\!\)
\(\underline{\underline{w}} \in \underline{\underline{W}}\!\)
|
\(\text{Abstract Feature}\!\)
\(\underline{\underline{w_i}} \in \underline{\underline{W}}\!\)
| |
\(\begin{matrix}
\underline{\underline{\text{A}}}
\\[4pt]
\underline{\underline{\text{B}}}
\\[4pt]
\underline{\underline{\text{a}}}
\\[4pt]
\underline{\underline{\text{b}}}
\\[4pt]
\underline{\underline{\text{i}}}
\\[4pt]
\underline{\underline{\text{u}}}
\end{matrix}\)
|
\(\begin{matrix}
\underline{\underline{o_1}}
\\[4pt]
\underline{\underline{o_2}}
\\[4pt]
\underline{\underline{s_1}}
\\[4pt]
\underline{\underline{s_2}}
\\[4pt]
\underline{\underline{s_3}}
\\[4pt]
\underline{\underline{s_4}}
\end{matrix}\)
|
\(\begin{matrix}
\underline{\underline{w_1}}
\\[4pt]
\underline{\underline{w_2}}
\\[4pt]
\underline{\underline{w_3}}
\\[4pt]
\underline{\underline{w_4}}
\\[4pt]
\underline{\underline{w_5}}
\\[4pt]
\underline{\underline{w_6}}
\end{matrix}\)
|
\(\text{Table 54.1} ~~ \text{Mnemonic Literal Codes for Interpreters A and B}\!\)
| \(\text{Element}\!\)
|
\(\text{Vector}\!\)
|
\(\text{Conjunct Term}\!\)
|
\(\text{Code}\!\)
| |
\(\begin{matrix}
\text{A}
\\[4pt]
\text{B}
\\[4pt]
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
100000
\\[4pt]
010000
\\[4pt]
001000
\\[4pt]
000100
\\[4pt]
000010
\\[4pt]
000001
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{A}}~
(\underline{\underline{B}})
(\underline{\underline{a}})
(\underline{\underline{b}})
(\underline{\underline{i}})
(\underline{\underline{u}})
\\[4pt]
(\underline{\underline{A}})
~\underline{\underline{B}}~
(\underline{\underline{a}})
(\underline{\underline{b}})
(\underline{\underline{i}})
(\underline{\underline{u}})
\\[4pt]
(\underline{\underline{A}})
(\underline{\underline{B}})
~\underline{\underline{a}}~
(\underline{\underline{b}})
(\underline{\underline{i}})
(\underline{\underline{u}})
\\[4pt]
(\underline{\underline{A}})
(\underline{\underline{B}})
(\underline{\underline{a}})
~\underline{\underline{b}}~
(\underline{\underline{i}})
(\underline{\underline{u}})
\\[4pt]
(\underline{\underline{A}})
(\underline{\underline{B}})
(\underline{\underline{a}})
(\underline{\underline{b}})
~\underline{\underline{i}}~
(\underline{\underline{u}})
\\[4pt]
(\underline{\underline{A}})
(\underline{\underline{B}})
(\underline{\underline{a}})
(\underline{\underline{b}})
(\underline{\underline{i}})
~\underline{\underline{u}}~
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{A}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{B}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{a}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{b}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{i}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{u}}\rangle}_W
\end{matrix}\)
|
\(\text{Table 54.2} ~~ \text{Pragmatic Literal Codes for Interpreters A and B}\!\)
| \(\text{Element}\!\)
|
\(\text{Vector}\!\)
|
\(\text{Conjunct Term}\!\)
|
\(\text{Code}\!\)
| |
\(\begin{matrix}
\text{A}
\\[4pt]
\text{B}
\\[4pt]
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
100000
\\[4pt]
010000
\\[4pt]
001000
\\[4pt]
000100
\\[4pt]
000010
\\[4pt]
000001
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{o_1}}~
(\underline{\underline{o_2}})
(\underline{\underline{s_1}})
(\underline{\underline{s_2}})
(\underline{\underline{s_3}})
(\underline{\underline{s_4}})
\\[4pt]
(\underline{\underline{o_1}})
~\underline{\underline{o_2}}~
(\underline{\underline{s_1}})
(\underline{\underline{s_2}})
(\underline{\underline{s_3}})
(\underline{\underline{s_4}})
\\[4pt]
(\underline{\underline{o_1}})
(\underline{\underline{o_2}})
~\underline{\underline{s_1}}~
(\underline{\underline{s_2}})
(\underline{\underline{s_3}})
(\underline{\underline{s_4}})
\\[4pt]
(\underline{\underline{o_1}})
(\underline{\underline{o_2}})
(\underline{\underline{s_1}})
~\underline{\underline{s_2}}~
(\underline{\underline{s_3}})
(\underline{\underline{s_4}})
\\[4pt]
(\underline{\underline{o_1}})
(\underline{\underline{o_2}})
(\underline{\underline{s_1}})
(\underline{\underline{s_2}})
~\underline{\underline{s_3}}~
(\underline{\underline{s_4}})
\\[4pt]
(\underline{\underline{o_1}})
(\underline{\underline{o_2}})
(\underline{\underline{s_1}})
(\underline{\underline{s_2}})
(\underline{\underline{s_3}})
~\underline{\underline{s_4}}~
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{o_1}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{o_2}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{s_1}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{s_2}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{s_3}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{s_4}}\rangle}_W
\end{matrix}\)
|
\(\text{Table 54.3} ~~ \text{Abstract Literal Codes for Interpreters A and B}\!\)
| \(\text{Element}\!\)
|
\(\text{Vector}\!\)
|
\(\text{Conjunct Term}\!\)
|
\(\text{Code}\!\)
| |
\(\begin{matrix}
\text{A}
\\[4pt]
\text{B}
\\[4pt]
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
100000
\\[4pt]
010000
\\[4pt]
001000
\\[4pt]
000100
\\[4pt]
000010
\\[4pt]
000001
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{w_1}}~
(\underline{\underline{w_2}})
(\underline{\underline{w_3}})
(\underline{\underline{w_4}})
(\underline{\underline{w_5}})
(\underline{\underline{w_6}})
\\[4pt]
(\underline{\underline{w_1}})
~\underline{\underline{w_2}}~
(\underline{\underline{w_3}})
(\underline{\underline{w_4}})
(\underline{\underline{w_5}})
(\underline{\underline{w_6}})
\\[4pt]
(\underline{\underline{w_1}})
(\underline{\underline{w_2}})
~\underline{\underline{w_3}}~
(\underline{\underline{w_4}})
(\underline{\underline{w_5}})
(\underline{\underline{w_6}})
\\[4pt]
(\underline{\underline{w_1}})
(\underline{\underline{w_2}})
(\underline{\underline{w_3}})
~\underline{\underline{w_4}}~
(\underline{\underline{w_5}})
(\underline{\underline{w_6}})
\\[4pt]
(\underline{\underline{w_1}})
(\underline{\underline{w_2}})
(\underline{\underline{w_3}})
(\underline{\underline{w_4}})
~\underline{\underline{w_5}}~
(\underline{\underline{w_6}})
\\[4pt]
(\underline{\underline{w_1}})
(\underline{\underline{w_2}})
(\underline{\underline{w_3}})
(\underline{\underline{w_4}})
(\underline{\underline{w_5}})
~\underline{\underline{w_6}}~
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{w_1}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{w_2}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{w_3}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{w_4}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{w_5}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{w_6}}\rangle}_W
\end{matrix}\)
|
\(\text{Table 55.1} ~~ \operatorname{LIR}_1 (L_\text{A}) : \text{Literal Representation of} ~ L_\text{A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{A}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\end{matrix}\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{B}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\end{matrix}\)
|
\(\text{Table 55.2} ~~ \operatorname{LIR}_1 (\operatorname{Den}(L_\text{A})) : \text{Denotative Component of} ~ L_\text{A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{A}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
({\langle\underline{\underline{\text{a}}}\rangle}_W,
{\langle\underline{\underline{\text{A}}}\rangle}_W)
\\[4pt]
({\langle\underline{\underline{\text{i}}}\rangle}_W,
{\langle\underline{\underline{\text{A}}}\rangle}_W)
\end{matrix}\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{B}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
({\langle\underline{\underline{\text{b}}}\rangle}_W,
{\langle\underline{\underline{\text{B}}}\rangle}_W)
\\[4pt]
({\langle\underline{\underline{\text{u}}}\rangle}_W,
{\langle\underline{\underline{\text{B}}}\rangle}_W)
\end{matrix}\)
|
\(\text{Table 55.3} ~~ \operatorname{LIR}_1 (\operatorname{Con}(L_\text{A})) : \text{Connotative Component of} ~ L_\text{A}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
0_{\operatorname{d}W}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{a}}}
~
\operatorname{d}\underline{\underline{\text{i}}}
\rangle}_{\operatorname{d}W}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{a}}}
~
\operatorname{d}\underline{\underline{\text{i}}}
\rangle}_{\operatorname{d}W}
\\[4pt]
0_{\operatorname{d}W}
\end{matrix}\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
0_{\operatorname{d}W}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{b}}}
~
\operatorname{d}\underline{\underline{\text{u}}}
\rangle}_{\operatorname{d}W}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{b}}}
~
\operatorname{d}\underline{\underline{\text{u}}}
\rangle}_{\operatorname{d}W}
\\[4pt]
0_{\operatorname{d}W}
\end{matrix}\)
|
\(\text{Table 56.1} ~~ \operatorname{LIR}_1 (L_\text{B}) : \text{Literal Representation of} ~ L_\text{B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{A}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\end{matrix}\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{B}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\end{matrix}\)
|
\(\text{Table 56.2} ~~ \operatorname{LIR}_1 (\operatorname{Den}(L_\text{B})) : \text{Denotative Component of} ~ L_\text{B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{A}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
({\langle\underline{\underline{\text{a}}}\rangle}_W,
{\langle\underline{\underline{\text{A}}}\rangle}_W)
\\[4pt]
({\langle\underline{\underline{\text{u}}}\rangle}_W,
{\langle\underline{\underline{\text{A}}}\rangle}_W)
\end{matrix}\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{B}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
({\langle\underline{\underline{\text{b}}}\rangle}_W,
{\langle\underline{\underline{\text{B}}}\rangle}_W)
\\[4pt]
({\langle\underline{\underline{\text{i}}}\rangle}_W,
{\langle\underline{\underline{\text{B}}}\rangle}_W)
\end{matrix}\)
|
\(\text{Table 56.3} ~~ \operatorname{LIR}_1 (\operatorname{Con}(L_\text{B})) : \text{Connotative Component of} ~ L_\text{B}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
0_{\operatorname{d}W}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{a}}}
~
\operatorname{d}\underline{\underline{\text{u}}}
\rangle}_{\operatorname{d}W}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{a}}}
~
\operatorname{d}\underline{\underline{\text{u}}}
\rangle}_{\operatorname{d}W}
\\[4pt]
0_{\operatorname{d}W}
\end{matrix}\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_W
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_W
\end{matrix}\)
|
\(\begin{matrix}
0_{\operatorname{d}W}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{b}}}
~
\operatorname{d}\underline{\underline{\text{i}}}
\rangle}_{\operatorname{d}W}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{b}}}
~
\operatorname{d}\underline{\underline{\text{i}}}
\rangle}_{\operatorname{d}W}
\\[4pt]
0_{\operatorname{d}W}
\end{matrix}\)
|
\(\text{Table 57.1} ~~ \text{Mnemonic Lateral Codes for Interpreters A and B}\!\)
| \(\text{Element}\!\)
|
\(\text{Vector}\!\)
|
\(\text{Conjunct Term}\!\)
|
\(\text{Code}\!\)
| |
\(\begin{matrix}
\text{A}
\\[4pt]
\text{B}
\\[4pt]
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{10}_X
\\[4pt]
{01}_X
\\[4pt]
{1000}_Y
\\[4pt]
{0100}_Y
\\[4pt]
{0010}_Y
\\[4pt]
{0001}_Y
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{A}}~
(\underline{\underline{B}})
\\[4pt]
(\underline{\underline{A}})
~\underline{\underline{B}}~
\\[4pt]
~\underline{\underline{a}}~
(\underline{\underline{b}})
(\underline{\underline{i}})
(\underline{\underline{u}})
\\[4pt]
(\underline{\underline{a}})
~\underline{\underline{b}}~
(\underline{\underline{i}})
(\underline{\underline{u}})
\\[4pt]
(\underline{\underline{a}})
(\underline{\underline{b}})
~\underline{\underline{i}}~
(\underline{\underline{u}})
\\[4pt]
(\underline{\underline{a}})
(\underline{\underline{b}})
(\underline{\underline{i}})
~\underline{\underline{u}}~
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{A}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{B}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{a}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{b}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{i}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{u}}\rangle}_Y
\end{matrix}\)
|
\(\text{Table 57.2} ~~ \text{Pragmatic Lateral Codes for Interpreters A and B}\!\)
| \(\text{Element}\!\)
|
\(\text{Vector}\!\)
|
\(\text{Conjunct Term}\!\)
|
\(\text{Code}\!\)
| |
\(\begin{matrix}
\text{A}
\\[4pt]
\text{B}
\\[4pt]
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{10}_X
\\[4pt]
{01}_X
\\[4pt]
{1000}_Y
\\[4pt]
{0100}_Y
\\[4pt]
{0010}_Y
\\[4pt]
{0001}_Y
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{o_1}}~
(\underline{\underline{o_2}})
\\[4pt]
(\underline{\underline{o_1}})
~\underline{\underline{o_2}}~
\\[4pt]
~\underline{\underline{s_1}}~
(\underline{\underline{s_2}})
(\underline{\underline{s_3}})
(\underline{\underline{s_4}})
\\[4pt]
(\underline{\underline{s_1}})
~\underline{\underline{s_2}}~
(\underline{\underline{s_3}})
(\underline{\underline{s_4}})
\\[4pt]
(\underline{\underline{s_1}})
(\underline{\underline{s_2}})
~\underline{\underline{s_3}}~
(\underline{\underline{s_4}})
\\[4pt]
(\underline{\underline{s_1}})
(\underline{\underline{s_2}})
(\underline{\underline{s_3}})
~\underline{\underline{s_4}}~
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{o_1}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{o_2}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{s_1}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{s_2}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{s_3}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{s_4}}\rangle}_Y
\end{matrix}\)
|
\(\text{Table 57.3} ~~ \text{Abstract Lateral Codes for Interpreters A and B}\!\)
| \(\text{Element}\!\)
|
\(\text{Vector}\!\)
|
\(\text{Conjunct Term}\!\)
|
\(\text{Code}\!\)
| |
\(\begin{matrix}
\text{A}
\\[4pt]
\text{B}
\\[4pt]
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{10}_X
\\[4pt]
{01}_X
\\[4pt]
{1000}_Y
\\[4pt]
{0100}_Y
\\[4pt]
{0010}_Y
\\[4pt]
{0001}_Y
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{x_1}}~
(\underline{\underline{x_2}})
\\[4pt]
(\underline{\underline{x_1}})
~\underline{\underline{x_2}}~
\\[4pt]
~\underline{\underline{y_1}}~
(\underline{\underline{y_2}})
(\underline{\underline{y_3}})
(\underline{\underline{y_4}})
\\[4pt]
(\underline{\underline{y_1}})
~\underline{\underline{y_2}}~
(\underline{\underline{y_3}})
(\underline{\underline{y_4}})
\\[4pt]
(\underline{\underline{y_1}})
(\underline{\underline{y_2}})
~\underline{\underline{y_3}}~
(\underline{\underline{y_4}})
\\[4pt]
(\underline{\underline{y_1}})
(\underline{\underline{y_2}})
(\underline{\underline{y_3}})
~\underline{\underline{y_4}}~
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{x_1}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{x_2}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{y_1}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{y_2}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{y_3}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{y_4}}\rangle}_Y
\end{matrix}\)
|
\(\text{Table 58.1} ~~ \operatorname{LIR}_2 (L_\text{A}) : \text{Lateral Representation of} ~ L_\text{A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
~\underline{\underline{\text{A}}}~
(\underline{\underline{\text{B}}})
\\[4pt]
~\underline{\underline{\text{A}}}~
(\underline{\underline{\text{B}}})
\\[4pt]
~\underline{\underline{\text{A}}}~
(\underline{\underline{\text{B}}})
\\[4pt]
~\underline{\underline{\text{A}}}~
(\underline{\underline{\text{B}}})
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\\[4pt]
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\end{matrix}\)
| |
\(\begin{matrix}
(\underline{\underline{\text{A}}})
~\underline{\underline{\text{B}}}~
\\[4pt]
(\underline{\underline{\text{A}}})
~\underline{\underline{\text{B}}}~
\\[4pt]
(\underline{\underline{\text{A}}})
~\underline{\underline{\text{B}}}~
\\[4pt]
(\underline{\underline{\text{A}}})
~\underline{\underline{\text{B}}}~
\end{matrix}\)
|
\(\begin{matrix}
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\end{matrix}\)
|
\(\begin{matrix}
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\\[4pt]
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\end{matrix}\)
|
\(\text{Table 58.2} ~~ \operatorname{LIR}_2 (\operatorname{Den}(L_\text{A})) : \text{Denotative Component of} ~ L_\text{A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
~\underline{\underline{\text{A}}}~
(\underline{\underline{\text{B}}})
\\[4pt]
~\underline{\underline{\text{A}}}~
(\underline{\underline{\text{B}}})
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\end{matrix}\)
|
\(\begin{matrix}
({\langle\underline{\underline{\text{a}}}\rangle}_Y,
{\langle\underline{\underline{\text{A}}}\rangle}_X)
\\[4pt]
({\langle\underline{\underline{\text{i}}}\rangle}_Y,
{\langle\underline{\underline{\text{A}}}\rangle}_X)
\end{matrix}\)
| |
\(\begin{matrix}
(\underline{\underline{\text{A}}})
~\underline{\underline{\text{B}}}~
\\[4pt]
(\underline{\underline{\text{A}}})
~\underline{\underline{\text{B}}}~
\end{matrix}\)
|
\(\begin{matrix}
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\end{matrix}\)
|
\(\begin{matrix}
({\langle\underline{\underline{\text{b}}}\rangle}_Y,
{\langle\underline{\underline{\text{B}}}\rangle}_X)
\\[4pt]
({\langle\underline{\underline{\text{u}}}\rangle}_Y,
{\langle\underline{\underline{\text{B}}}\rangle}_X)
\end{matrix}\)
|
\(\text{Table 58.3} ~~ \operatorname{LIR}_2 (\operatorname{Con}(L_\text{A})) : \text{Connotative Component of} ~ L_\text{A}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\\[4pt]
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\end{matrix}\)
|
\(\begin{matrix}
(\underline{\underline{\text{da}}})
(\underline{\underline{\text{db}}})
(\underline{\underline{\text{di}}})
(\underline{\underline{\text{du}}})
\\[4pt]
~\underline{\underline{\text{da}}}~
(\underline{\underline{\text{db}}})
~\underline{\underline{\text{di}}}~
(\underline{\underline{\text{du}}})
\\[4pt]
~\underline{\underline{\text{da}}}~
(\underline{\underline{\text{db}}})
~\underline{\underline{\text{di}}}~
(\underline{\underline{\text{du}}})
\\[4pt]
(\underline{\underline{\text{da}}})
(\underline{\underline{\text{db}}})
(\underline{\underline{\text{di}}})
(\underline{\underline{\text{du}}})
\end{matrix}\)
| |
\(\begin{matrix}
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\end{matrix}\)
|
\(\begin{matrix}
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\\[4pt]
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\end{matrix}\)
|
\(\begin{matrix}
(\underline{\underline{\text{da}}})
(\underline{\underline{\text{db}}})
(\underline{\underline{\text{di}}})
(\underline{\underline{\text{du}}})
\\[4pt]
(\underline{\underline{\text{da}}})
~\underline{\underline{\text{db}}}~
(\underline{\underline{\text{di}}})
~\underline{\underline{\text{du}}}~
\\[4pt]
(\underline{\underline{\text{da}}})
~\underline{\underline{\text{db}}}~
(\underline{\underline{\text{di}}})
~\underline{\underline{\text{du}}}~
\\[4pt]
(\underline{\underline{\text{da}}})
(\underline{\underline{\text{db}}})
(\underline{\underline{\text{di}}})
(\underline{\underline{\text{du}}})
\end{matrix}\)
|
\(\text{Table 59.1} ~~ \operatorname{LIR}_2 (L_\text{B}) : \text{Lateral Representation of} ~ L_\text{B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
~\underline{\underline{\text{A}}}~
(\underline{\underline{\text{B}}})
\\[4pt]
~\underline{\underline{\text{A}}}~
(\underline{\underline{\text{B}}})
\\[4pt]
~\underline{\underline{\text{A}}}~
(\underline{\underline{\text{B}}})
\\[4pt]
~\underline{\underline{\text{A}}}~
(\underline{\underline{\text{B}}})
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\\[4pt]
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\end{matrix}\)
| |
\(\begin{matrix}
(\underline{\underline{\text{A}}})
~\underline{\underline{\text{B}}}~
\\[4pt]
(\underline{\underline{\text{A}}})
~\underline{\underline{\text{B}}}~
\\[4pt]
(\underline{\underline{\text{A}}})
~\underline{\underline{\text{B}}}~
\\[4pt]
(\underline{\underline{\text{A}}})
~\underline{\underline{\text{B}}}~
\end{matrix}\)
|
\(\begin{matrix}
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\end{matrix}\)
|
\(\begin{matrix}
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\end{matrix}\)
|
\(\text{Table 59.2} ~~ \operatorname{LIR}_2 (\operatorname{Den}(L_\text{B})) : \text{Denotative Component of} ~ L_\text{B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
~\underline{\underline{\text{A}}}~
(\underline{\underline{\text{B}}})
\\[4pt]
~\underline{\underline{\text{A}}}~
(\underline{\underline{\text{B}}})
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\end{matrix}\)
|
\(\begin{matrix}
({\langle\underline{\underline{\text{a}}}\rangle}_Y,
{\langle\underline{\underline{\text{A}}}\rangle}_X)
\\[4pt]
({\langle\underline{\underline{\text{u}}}\rangle}_Y,
{\langle\underline{\underline{\text{A}}}\rangle}_X)
\end{matrix}\)
| |
\(\begin{matrix}
(\underline{\underline{\text{A}}})
~\underline{\underline{\text{B}}}~
\\[4pt]
(\underline{\underline{\text{A}}})
~\underline{\underline{\text{B}}}~
\end{matrix}\)
|
\(\begin{matrix}
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\end{matrix}\)
|
\(\begin{matrix}
({\langle\underline{\underline{\text{b}}}\rangle}_Y,
{\langle\underline{\underline{\text{B}}}\rangle}_X)
\\[4pt]
({\langle\underline{\underline{\text{i}}}\rangle}_Y,
{\langle\underline{\underline{\text{B}}}\rangle}_X)
\end{matrix}\)
|
\(\text{Table 59.3} ~~ \operatorname{LIR}_2 (\operatorname{Con}(L_\text{B})) : \text{Connotative Component of} ~ L_\text{B}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\end{matrix}\)
|
\(\begin{matrix}
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\\[4pt]
~\underline{\underline{\text{a}}}~
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
(\underline{\underline{\text{i}}})
~\underline{\underline{\text{u}}}~
\end{matrix}\)
|
\(\begin{matrix}
(\underline{\underline{\text{da}}})
(\underline{\underline{\text{db}}})
(\underline{\underline{\text{di}}})
(\underline{\underline{\text{du}}})
\\[4pt]
~\underline{\underline{\text{da}}}~
(\underline{\underline{\text{db}}})
(\underline{\underline{\text{di}}})
~\underline{\underline{\text{du}}}~
\\[4pt]
~\underline{\underline{\text{da}}}~
(\underline{\underline{\text{db}}})
(\underline{\underline{\text{di}}})
~\underline{\underline{\text{du}}}~
\\[4pt]
(\underline{\underline{\text{da}}})
(\underline{\underline{\text{db}}})
(\underline{\underline{\text{di}}})
(\underline{\underline{\text{du}}})
\end{matrix}\)
| |
\(\begin{matrix}
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\end{matrix}\)
|
\(\begin{matrix}
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
~\underline{\underline{\text{b}}}~
(\underline{\underline{\text{i}}})
(\underline{\underline{\text{u}}})
\\[4pt]
(\underline{\underline{\text{a}}})
(\underline{\underline{\text{b}}})
~\underline{\underline{\text{i}}}~
(\underline{\underline{\text{u}}})
\end{matrix}\)
|
\(\begin{matrix}
(\underline{\underline{\text{da}}})
(\underline{\underline{\text{db}}})
(\underline{\underline{\text{di}}})
(\underline{\underline{\text{du}}})
\\[4pt]
(\underline{\underline{\text{da}}})
~\underline{\underline{\text{db}}}~
~\underline{\underline{\text{di}}}~
(\underline{\underline{\text{du}}})
\\[4pt]
(\underline{\underline{\text{da}}})
~\underline{\underline{\text{db}}}~
~\underline{\underline{\text{di}}}~
(\underline{\underline{\text{du}}})
\\[4pt]
(\underline{\underline{\text{da}}})
(\underline{\underline{\text{db}}})
(\underline{\underline{\text{di}}})
(\underline{\underline{\text{du}}})
\end{matrix}\)
|
\(\text{Table 60.1} ~~ \operatorname{LIR}_3 (L_\text{A}) : \text{Lateral Representation of} ~ L_\text{A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{A}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\end{matrix}\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{B}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\end{matrix}\)
|
\(\text{Table 60.2} ~~ \operatorname{LIR}_3 (\operatorname{Den}(L_\text{A})) : \text{Denotative Component of} ~ L_\text{A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{A}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
({\langle\underline{\underline{\text{a}}}\rangle}_Y,
{\langle\underline{\underline{\text{A}}}\rangle}_X)
\\[4pt]
({\langle\underline{\underline{\text{i}}}\rangle}_Y,
{\langle\underline{\underline{\text{A}}}\rangle}_X)
\end{matrix}\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{B}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
({\langle\underline{\underline{\text{b}}}\rangle}_Y,
{\langle\underline{\underline{\text{B}}}\rangle}_X)
\\[4pt]
({\langle\underline{\underline{\text{u}}}\rangle}_Y,
{\langle\underline{\underline{\text{B}}}\rangle}_X)
\end{matrix}\)
|
\(\text{Table 60.3} ~~ \operatorname{LIR}_3 (\operatorname{Con}(L_\text{A})) : \text{Connotative Component of} ~ L_\text{A}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
0_{\operatorname{d}Y}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{a}}}
~
\operatorname{d}\underline{\underline{\text{i}}}
\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{a}}}
~
\operatorname{d}\underline{\underline{\text{i}}}
\rangle}_{\operatorname{d}Y}
\\[4pt]
0_{\operatorname{d}Y}
\end{matrix}\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
0_{\operatorname{d}Y}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{b}}}
~
\operatorname{d}\underline{\underline{\text{u}}}
\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{b}}}
~
\operatorname{d}\underline{\underline{\text{u}}}
\rangle}_{\operatorname{d}Y}
\\[4pt]
0_{\operatorname{d}Y}
\end{matrix}\)
|
\(\text{Table 61.1} ~~ \operatorname{LIR}_3 (L_\text{B}) : \text{Lateral Representation of} ~ L_\text{B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{A}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\end{matrix}\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{B}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\end{matrix}\)
|
\(\text{Table 61.2} ~~ \operatorname{LIR}_3 (\operatorname{Den}(L_\text{B})) : \text{Denotative Component of} ~ L_\text{B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{A}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{A}}}\rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
({\langle\underline{\underline{\text{a}}}\rangle}_Y,
{\langle\underline{\underline{\text{A}}}\rangle}_X)
\\[4pt]
({\langle\underline{\underline{\text{u}}}\rangle}_Y,
{\langle\underline{\underline{\text{A}}}\rangle}_X)
\end{matrix}\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{B}}}\rangle}_X
\\[4pt]
{\langle\underline{\underline{\text{B}}}\rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
({\langle\underline{\underline{\text{b}}}\rangle}_Y,
{\langle\underline{\underline{\text{B}}}\rangle}_X)
\\[4pt]
({\langle\underline{\underline{\text{i}}}\rangle}_Y,
{\langle\underline{\underline{\text{B}}}\rangle}_X)
\end{matrix}\)
|
\(\text{Table 61.3} ~~ \operatorname{LIR}_3 (\operatorname{Con}(L_\text{B})) : \text{Connotative Component of} ~ L_\text{B}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{a}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{u}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
0_{\operatorname{d}Y}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{a}}}
~
\operatorname{d}\underline{\underline{\text{u}}}
\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{a}}}
~
\operatorname{d}\underline{\underline{\text{u}}}
\rangle}_{\operatorname{d}Y}
\\[4pt]
0_{\operatorname{d}Y}
\end{matrix}\)
| |
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{b}}}\rangle}_Y
\\[4pt]
{\langle\underline{\underline{\text{i}}}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
0_{\operatorname{d}Y}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{b}}}
~
\operatorname{d}\underline{\underline{\text{i}}}
\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle
\operatorname{d}\underline{\underline{\text{b}}}
~
\operatorname{d}\underline{\underline{\text{i}}}
\rangle}_{\operatorname{d}Y}
\\[4pt]
0_{\operatorname{d}Y}
\end{matrix}\)
|
\(\text{Table 62.1} ~~ \text{Analytic Codes for Object Features}\!\)
| \(\text{Category}\!\)
|
\(\text{Mnemonic}\!\)
|
\(\text{Code}\!\)
| |
\(\begin{array}{l}
\text{Self}
\\[4pt]
\text{Other}
\end{array}\)
|
\(\begin{matrix}
\text{self}
\\[4pt]
\text{(self)}
\end{matrix}\)
|
\(\begin{matrix}
\text{s}
\\[4pt]
\text{(s)}
\end{matrix}\)
|
\(\text{Table 62.2} ~~ \text{Analytic Codes for Semantic Features}\!\)
| \(\text{Category}\!\)
|
\(\text{Mnemonic}\!\)
|
\(\text{Code}\!\)
| |
\(\begin{array}{l}
\text{1st Person}
\\[4pt]
\text{2nd Person}
\end{array}\)
|
\(\begin{matrix}
\text{my}
\\[4pt]
\text{(my)}
\end{matrix}\)
|
\(\begin{matrix}
\text{m}
\\[4pt]
\text{(m)}
\end{matrix}\)
|
\(\text{Table 62.3} ~~ \text{Analytic Codes for Syntactic Features}\!\)
| \(\text{Category}\!\)
|
\(\text{Mnemonic}\!\)
|
\(\text{Code}\!\)
| |
\(\begin{array}{l}
\text{Noun}
\\[4pt]
\text{Pronoun}
\end{array}\)
|
\(\begin{matrix}
\text{name}
\\[4pt]
\text{(name)}
\end{matrix}\)
|
\(\begin{matrix}
\text{n}
\\[4pt]
\text{(n)}
\end{matrix}\)
|
\(\text{Table 63.} ~~ \text{Analytic Codes for Interpreter A}\!\)
| \(\text{Name}\!\)
|
\(\text{Vector}\!\)
|
\(\text{Conjunct Term}\!\)
|
\(\text{Mnemonic}\!\)
|
\(\text{Code}\!\)
| |
\(\begin{matrix}
\text{A}
\\[4pt]
\text{B}
\\[4pt]
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{1}_X
\\[4pt]
{0}_X
\\[4pt]
{11}_Y
\\[4pt]
{01}_Y
\\[4pt]
{10}_Y
\\[4pt]
{00}_Y
\end{matrix}\)
|
\(\begin{matrix}
~x_1~
\\[4pt]
(x_1)
\\[4pt]
~y_1~~y_2~
\\[4pt]
(y_1)~y_2~
\\[4pt]
~y_1~(y_2)
\\[4pt]
(y_1)(y_2)
\end{matrix}\)
|
\(\begin{matrix}
~\text{self}~
\\[4pt]
(\text{self})
\\[4pt]
~\text{my}~~\text{name}~
\\[4pt]
(\text{my})~\text{name}~
\\[4pt]
~\text{my}~(\text{name})
\\[4pt]
(\text{my})(\text{name})
\end{matrix}\)
|
\(\begin{matrix}
~\text{s}~
\\[4pt]
(\text{s})
\\[4pt]
~\text{m}~~\text{n}~
\\[4pt]
(\text{m})~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\\[4pt]
(\text{m})(\text{n})
\end{matrix}\)
|
\(\text{Table 64.} ~~ \text{Analytic Codes for Interpreter B}\!\)
| \(\text{Name}\!\)
|
\(\text{Vector}\!\)
|
\(\text{Conjunct Term}\!\)
|
\(\text{Mnemonic}\!\)
|
\(\text{Code}\!\)
| |
\(\begin{matrix}
\text{A}
\\[4pt]
\text{B}
\\[4pt]
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\[4pt]
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{0}_X
\\[4pt]
{1}_X
\\[4pt]
{01}_Y
\\[4pt]
{11}_Y
\\[4pt]
{10}_Y
\\[4pt]
{00}_Y
\end{matrix}\)
|
\(\begin{matrix}
(x_1)
\\[4pt]
~x_1~
\\[4pt]
(y_1)~y_2~
\\[4pt]
~y_1~~y_2~
\\[4pt]
~y_1~(y_2)
\\[4pt]
(y_1)(y_2)
\end{matrix}\)
|
\(\begin{matrix}
(\text{self})
\\[4pt]
~\text{self}~
\\[4pt]
(\text{my})~\text{name}~
\\[4pt]
~\text{my}~~\text{name}~
\\[4pt]
~\text{my}~(\text{name})
\\[4pt]
(\text{my})(\text{name})
\end{matrix}\)
|
\(\begin{matrix}
(\text{s})
\\[4pt]
~\text{s}~
\\[4pt]
(\text{m})~\text{n}~
\\[4pt]
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\\[4pt]
(\text{m})(\text{n})
\end{matrix}\)
|
\(\text{Table 65.1} ~~ \operatorname{AIR}_1 (L_\text{A}) : \text{Analytic Representation of} ~ L_\text{A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{s}
\\[4pt]
\text{s}
\\[4pt]
\text{s}
\\[4pt]
\text{s}
\end{matrix}\)
|
\(\begin{matrix}
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\\[4pt]
~\text{m}~(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\\[4pt]
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\end{matrix}\)
| |
\(\begin{matrix}
(\text{s})
\\[4pt]
(\text{s})
\\[4pt]
(\text{s})
\\[4pt]
(\text{s})
\end{matrix}\)
|
\(\begin{matrix}
(\text{m})~\text{n}~
\\[4pt]
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\\[4pt]
(\text{m})(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\\[4pt]
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\end{matrix}\)
|
\(\text{Table 65.2} ~~ \operatorname{AIR}_1 (\operatorname{Den}(L_\text{A})) : \text{Denotative Component of} ~ L_\text{A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
\text{s}
\\[4pt]
\text{s}
\end{matrix}\)
|
\(\begin{matrix}
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
~\text{m}~~\text{n}~ \mapsto ~\text{s}~
\\[4pt]
~\text{m}~(\text{n}) \mapsto ~\text{s}~
\end{matrix}\)
| |
\(\begin{matrix}
(\text{s})
\\[4pt]
(\text{s})
\end{matrix}\)
|
\(\begin{matrix}
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
(\text{m})~\text{n}~ \mapsto (\text{s})
\\[4pt]
(\text{m})(\text{n}) \mapsto (\text{s})
\end{matrix}\)
|
\(\text{Table 65.3} ~~ \operatorname{AIR}_1 (\operatorname{Con}(L_\text{A})) : \text{Connotative Component of} ~ L_\text{A}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\\[4pt]
~\text{m}~(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\\[4pt]
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
(\text{dm})(\text{dn})
\\[4pt]
(\text{dm})~\text{dn}~
\\[4pt]
(\text{dm})~\text{dn}~
\\[4pt]
(\text{dm})(\text{dn})
\end{matrix}\)
| |
\(\begin{matrix}
(\text{m})~\text{n}~
\\[4pt]
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\\[4pt]
(\text{m})(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\\[4pt]
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
(\text{dm})(\text{dn})
\\[4pt]
(\text{dm})~\text{dn}~
\\[4pt]
(\text{dm})~\text{dn}~
\\[4pt]
(\text{dm})(\text{dn})
\end{matrix}\)
|
\(\text{Table 66.1} ~~ \operatorname{AIR}_1 (L_\text{B}) : \text{Analytic Representation of} ~ L_\text{B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
(\text{s})
\\[4pt]
(\text{s})
\\[4pt]
(\text{s})
\\[4pt]
(\text{s})
\end{matrix}\)
|
\(\begin{matrix}
(\text{m})~\text{n}~
\\[4pt]
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\\[4pt]
(\text{m})(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\\[4pt]
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\end{matrix}\)
| |
\(\begin{matrix}
\text{s}
\\[4pt]
\text{s}
\\[4pt]
\text{s}
\\[4pt]
\text{s}
\end{matrix}\)
|
\(\begin{matrix}
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\\[4pt]
~\text{m}~(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\\[4pt]
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\end{matrix}\)
|
\(\text{Table 66.2} ~~ \operatorname{AIR}_1 (\operatorname{Den}(L_\text{B})) : \text{Denotative Component of} ~ L_\text{B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
(\text{s})
\\[4pt]
(\text{s})
\end{matrix}\)
|
\(\begin{matrix}
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
(\text{m})~\text{n}~ \mapsto (\text{s})
\\[4pt]
(\text{m})(\text{n}) \mapsto (\text{s})
\end{matrix}\)
| |
\(\begin{matrix}
\text{s}
\\[4pt]
\text{s}
\end{matrix}\)
|
\(\begin{matrix}
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
~\text{m}~~\text{n}~ \mapsto ~\text{s}~
\\[4pt]
~\text{m}~(\text{n}) \mapsto ~\text{s}~
\end{matrix}\)
|
\(\text{Table 66.3} ~~ \operatorname{AIR}_1 (\operatorname{Con}(L_\text{B})) : \text{Connotative Component of} ~ L_\text{B}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
(\text{m})~\text{n}~
\\[4pt]
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\\[4pt]
(\text{m})(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\\[4pt]
(\text{m})~\text{n}~
\\[4pt]
(\text{m})(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
(\text{dm})(\text{dn})
\\[4pt]
(\text{dm})~\text{dn}~
\\[4pt]
(\text{dm})~\text{dn}~
\\[4pt]
(\text{dm})(\text{dn})
\end{matrix}\)
| |
\(\begin{matrix}
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\\[4pt]
~\text{m}~(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\\[4pt]
~\text{m}~~\text{n}~
\\[4pt]
~\text{m}~(\text{n})
\end{matrix}\)
|
\(\begin{matrix}
(\text{dm})(\text{dn})
\\[4pt]
(\text{dm})~\text{dn}~
\\[4pt]
(\text{dm})~\text{dn}~
\\[4pt]
(\text{dm})(\text{dn})
\end{matrix}\)
|
\(\text{Table 67.1} ~~ \operatorname{AIR}_2 (L_\text{A}) : \text{Analytic Representation of} ~ L_\text{A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
{\langle * \rangle}_X
\\[4pt]
{\langle * \rangle}_X
\\[4pt]
{\langle * \rangle}_X
\\[4pt]
{\langle * \rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle * \rangle}_Y
\\[4pt]
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\\[4pt]
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\end{matrix}\)
| |
\(\begin{matrix}
{\langle ! \rangle}_X
\\[4pt]
{\langle ! \rangle}_X
\\[4pt]
{\langle ! \rangle}_X
\\[4pt]
{\langle ! \rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\\[4pt]
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\end{matrix}\)
|
\(\text{Table 67.2} ~~ \operatorname{AIR}_2 (\operatorname{Den}(L_\text{A})) : \text{Denotative Component of} ~ L_\text{A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{\langle * \rangle}_X
\\[4pt]
{\langle * \rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\end{matrix}\)
|
\(\begin{array}{r}
{\langle * \rangle}_Y \mapsto {\langle * \rangle}_X
\\[4pt]
{\langle\text{m}\rangle}_Y \mapsto {\langle * \rangle}_X
\end{array}\)
| |
\(\begin{matrix}
{\langle ! \rangle}_X
\\[4pt]
{\langle ! \rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\end{matrix}\)
|
\(\begin{array}{r}
{\langle\text{n}\rangle}_Y \mapsto {\langle ! \rangle}_X
\\[4pt]
{\langle ! \rangle}_Y \mapsto {\langle ! \rangle}_X
\end{array}\)
|
\(\text{Table 67.3} ~~ \operatorname{AIR}_2 (\operatorname{Con}(L_\text{A})) : \text{Connotative Component of} ~ L_\text{A}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{\langle * \rangle}_Y
\\[4pt]
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\\[4pt]
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\operatorname{d}!\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle\operatorname{d}!\rangle}_{\operatorname{d}Y}
\end{matrix}\)
| |
\(\begin{matrix}
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\\[4pt]
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\operatorname{d}!\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle\operatorname{d}!\rangle}_{\operatorname{d}Y}
\end{matrix}\)
|
\(\text{Table 68.1} ~~ \operatorname{AIR}_2 (L_\text{B}) : \text{Analytic Representation of} ~ L_\text{B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
{\langle ! \rangle}_X
\\[4pt]
{\langle ! \rangle}_X
\\[4pt]
{\langle ! \rangle}_X
\\[4pt]
{\langle ! \rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\\[4pt]
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\end{matrix}\)
| |
\(\begin{matrix}
{\langle * \rangle}_X
\\[4pt]
{\langle * \rangle}_X
\\[4pt]
{\langle * \rangle}_X
\\[4pt]
{\langle * \rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle * \rangle}_Y
\\[4pt]
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\\[4pt]
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\end{matrix}\)
|
\(\text{Table 68.2} ~~ \operatorname{AIR}_2 (\operatorname{Den}(L_\text{B})) : \text{Denotative Component of} ~ L_\text{B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{\langle ! \rangle}_X
\\[4pt]
{\langle ! \rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\end{matrix}\)
|
\(\begin{array}{r}
{\langle\text{n}\rangle}_Y \mapsto {\langle ! \rangle}_X
\\[4pt]
{\langle ! \rangle}_Y \mapsto {\langle ! \rangle}_X
\end{array}\)
| |
\(\begin{matrix}
{\langle * \rangle}_X
\\[4pt]
{\langle * \rangle}_X
\end{matrix}\)
|
\(\begin{matrix}
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\end{matrix}\)
|
\(\begin{array}{r}
{\langle * \rangle}_Y \mapsto {\langle * \rangle}_X
\\[4pt]
{\langle\text{m}\rangle}_Y \mapsto {\langle * \rangle}_X
\end{array}\)
|
\(\text{Table 68.3} ~~ \operatorname{AIR}_2 (\operatorname{Con}(L_\text{B})) : \text{Connotative Component of} ~ L_\text{B}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
|
\(\text{Transition}\!\)
| |
\(\begin{matrix}
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\\[4pt]
{\langle\text{n}\rangle}_Y
\\[4pt]
{\langle ! \rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\operatorname{d}!\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle\operatorname{d}!\rangle}_{\operatorname{d}Y}
\end{matrix}\)
| |
\(\begin{matrix}
{\langle * \rangle}_Y
\\[4pt]
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\\[4pt]
{\langle * \rangle}_Y
\\[4pt]
{\langle\text{m}\rangle}_Y
\end{matrix}\)
|
\(\begin{matrix}
{\langle\operatorname{d}!\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y}
\\[4pt]
{\langle\operatorname{d}!\rangle}_{\operatorname{d}Y}
\end{matrix}\)
|
\(\text{Table 69.} ~~ \text{Schematism of Sequential Inference}\!\)
| \(\text{Initial Premiss}\!\)
|
\(\text{Differential Premiss}\!\)
|
\(\text{Inferred Sequel}\!\)
| |
\(\begin{matrix}
~x~ ~\operatorname{at}~ t
\\[4pt]
~x~ ~\operatorname{at}~ t
\\[4pt]
(x) ~\operatorname{at}~ t
\\[4pt]
(x) ~\operatorname{at}~ t
\end{matrix}\)
|
\(\begin{matrix}
~\operatorname{d}x~ ~\operatorname{at}~ t
\\[4pt]
(\operatorname{d}x) ~\operatorname{at}~ t
\\[4pt]
~\operatorname{d}x~ ~\operatorname{at}~ t
\\[4pt]
(\operatorname{d}x) ~\operatorname{at}~ t
\end{matrix}\)
|
\(\begin{matrix}
(x) ~\operatorname{at}~ t'
\\[4pt]
~x~ ~\operatorname{at}~ t'
\\[4pt]
~x~ ~\operatorname{at}~ t'
\\[4pt]
(x) ~\operatorname{at}~ t'
\end{matrix}\)
|
\(\text{Table 70.1} ~~ \text{Group Representation} ~ \operatorname{Rep}^\text{A} (V_4)\!\)
| \(\begin{matrix} \text{Abstract} \\ \text{Element} \end{matrix}\)
|
\(\begin{matrix} \text{Logical} \\ \text{Element} \end{matrix}\)
|
\(\begin{matrix} \text{Active} \\ \text{List} \end{matrix}\)
|
\(\begin{matrix} \text{Active} \\ \text{Term} \end{matrix}\)
|
\(\begin{matrix} \text{Genetic} \\ \text{Element} \end{matrix}\)
| |
\(\begin{matrix}
1
\\[4pt]
r
\\[4pt]
s
\\[4pt]
t
\end{matrix}\)
|
\(\begin{matrix}
(\operatorname{d}\underline{\underline{\text{a}}})
(\operatorname{d}\underline{\underline{\text{b}}})
(\operatorname{d}\underline{\underline{\text{i}}})
(\operatorname{d}\underline{\underline{\text{u}}})
\\[4pt]
~\operatorname{d}\underline{\underline{\text{a}}}~
(\operatorname{d}\underline{\underline{\text{b}}})
~\operatorname{d}\underline{\underline{\text{i}}}~
(\operatorname{d}\underline{\underline{\text{u}}})
\\[4pt]
(\operatorname{d}\underline{\underline{\text{a}}})
~\operatorname{d}\underline{\underline{\text{b}}}~
(\operatorname{d}\underline{\underline{\text{i}}})
~\operatorname{d}\underline{\underline{\text{u}}}~
\\[4pt]
~\operatorname{d}\underline{\underline{\text{a}}}~
~\operatorname{d}\underline{\underline{\text{b}}}~
~\operatorname{d}\underline{\underline{\text{i}}}~
~\operatorname{d}\underline{\underline{\text{u}}}~
\end{matrix}\)
|
\(\begin{matrix}
\langle \operatorname{d}! \rangle
\\[4pt]
\langle
\operatorname{d}\underline{\underline{\text{a}}} ~
\operatorname{d}\underline{\underline{\text{i}}}
\rangle
\\[4pt]
\langle
\operatorname{d}\underline{\underline{\text{b}}} ~
\operatorname{d}\underline{\underline{\text{u}}}
\rangle
\\[4pt]
\langle \operatorname{d}* \rangle
\end{matrix}\)
|
\(\begin{matrix}
\operatorname{d}!
\\[4pt]
\operatorname{d}\underline{\underline{\text{a}}} \cdot
\operatorname{d}\underline{\underline{\text{i}}} ~ !
\\[4pt]
\operatorname{d}\underline{\underline{\text{b}}} \cdot
\operatorname{d}\underline{\underline{\text{u}}} ~ !
\\[4pt]
\operatorname{d}*
\end{matrix}\)
|
\(\begin{matrix}
1
\\[4pt]
\operatorname{d}_{\text{ai}}
\\[4pt]
\operatorname{d}_{\text{bu}}
\\[4pt]
\operatorname{d}_{\text{ai}} * \operatorname{d}_{\text{bu}}
\end{matrix}\)
|
\(\text{Table 70.2} ~~ \text{Group Representation} ~ \operatorname{Rep}^\text{B} (V_4)\!\)
| \(\begin{matrix} \text{Abstract} \\ \text{Element} \end{matrix}\)
|
\(\begin{matrix} \text{Logical} \\ \text{Element} \end{matrix}\)
|
\(\begin{matrix} \text{Active} \\ \text{List} \end{matrix}\)
|
\(\begin{matrix} \text{Active} \\ \text{Term} \end{matrix}\)
|
\(\begin{matrix} \text{Genetic} \\ \text{Element} \end{matrix}\)
| |
\(\begin{matrix}
1
\\[4pt]
r
\\[4pt]
s
\\[4pt]
t
\end{matrix}\)
|
\(\begin{matrix}
(\operatorname{d}\underline{\underline{\text{a}}})
(\operatorname{d}\underline{\underline{\text{b}}})
(\operatorname{d}\underline{\underline{\text{i}}})
(\operatorname{d}\underline{\underline{\text{u}}})
\\[4pt]
~\operatorname{d}\underline{\underline{\text{a}}}~
(\operatorname{d}\underline{\underline{\text{b}}})
(\operatorname{d}\underline{\underline{\text{i}}})
~\operatorname{d}\underline{\underline{\text{u}}}~
\\[4pt]
(\operatorname{d}\underline{\underline{\text{a}}})
~\operatorname{d}\underline{\underline{\text{b}}}~
~\operatorname{d}\underline{\underline{\text{i}}}~
(\operatorname{d}\underline{\underline{\text{u}}})
\\[4pt]
~\operatorname{d}\underline{\underline{\text{a}}}~
~\operatorname{d}\underline{\underline{\text{b}}}~
~\operatorname{d}\underline{\underline{\text{i}}}~
~\operatorname{d}\underline{\underline{\text{u}}}~
\end{matrix}\)
|
\(\begin{matrix}
\langle \operatorname{d}! \rangle
\\[4pt]
\langle
\operatorname{d}\underline{\underline{\text{a}}} ~
\operatorname{d}\underline{\underline{\text{u}}}
\rangle
\\[4pt]
\langle
\operatorname{d}\underline{\underline{\text{b}}} ~
\operatorname{d}\underline{\underline{\text{i}}}
\rangle
\\[4pt]
\langle \operatorname{d}* \rangle
\end{matrix}\)
|
\(\begin{matrix}
\operatorname{d}!
\\[4pt]
\operatorname{d}\underline{\underline{\text{a}}} \cdot
\operatorname{d}\underline{\underline{\text{u}}} ~ !
\\[4pt]
\operatorname{d}\underline{\underline{\text{b}}} \cdot
\operatorname{d}\underline{\underline{\text{i}}} ~ !
\\[4pt]
\operatorname{d}*
\end{matrix}\)
|
\(\begin{matrix}
1
\\[4pt]
\operatorname{d}_{\text{au}}
\\[4pt]
\operatorname{d}_{\text{bi}}
\\[4pt]
\operatorname{d}_{\text{au}} * \operatorname{d}_{\text{bi}}
\end{matrix}\)
|
\(\text{Table 70.3} ~~ \text{Group Representation} ~ \operatorname{Rep}^\text{C} (V_4)\!\)
| \(\begin{matrix} \text{Abstract} \\ \text{Element} \end{matrix}\)
|
\(\begin{matrix} \text{Logical} \\ \text{Element} \end{matrix}\)
|
\(\begin{matrix} \text{Active} \\ \text{List} \end{matrix}\)
|
\(\begin{matrix} \text{Active} \\ \text{Term} \end{matrix}\)
|
\(\begin{matrix} \text{Genetic} \\ \text{Element} \end{matrix}\)
| |
\(\begin{matrix}
1
\\[4pt]
r
\\[4pt]
s
\\[4pt]
t
\end{matrix}\)
|
\(\begin{matrix}
(\operatorname{d}\text{m})
(\operatorname{d}\text{n})
\\[4pt]
~\operatorname{d}\text{m}~
(\operatorname{d}\text{n})
\\[4pt]
(\operatorname{d}\text{m})
~\operatorname{d}\text{n}~
\\[4pt]
~\operatorname{d}\text{m}~
~\operatorname{d}\text{n}~
\end{matrix}\)
|
\(\begin{matrix}
\langle\operatorname{d}!\rangle
\\[4pt]
\langle\operatorname{d}\text{m}\rangle
\\[4pt]
\langle\operatorname{d}\text{n}\rangle
\\[4pt]
\langle\operatorname{d}*\rangle
\end{matrix}\)
|
\(\begin{matrix}
\operatorname{d}!
\\[4pt]
\operatorname{d}\text{m}!
\\[4pt]
\operatorname{d}\text{n}!
\\[4pt]
\operatorname{d}*
\end{matrix}\)
|
\(\begin{matrix}
1
\\[4pt]
\operatorname{d}_{\text{m}}
\\[4pt]
\operatorname{d}_{\text{n}}
\\[4pt]
\operatorname{d}_{\text{m}} * \operatorname{d}_{\text{n}}
\end{matrix}\)
|
\(\text{Table 71.1} ~~ \text{The Differential Group} ~ G = V_4\!\)
| \(\begin{matrix} \text{Abstract} \\ \text{Element} \end{matrix}\)
|
\(\begin{matrix} \text{Logical} \\ \text{Element} \end{matrix}\)
|
\(\begin{matrix} \text{Active} \\ \text{List} \end{matrix}\)
|
\(\begin{matrix} \text{Active} \\ \text{Term} \end{matrix}\)
|
\(\begin{matrix} \text{Genetic} \\ \text{Element} \end{matrix}\)
| |
\(\begin{matrix}
1
\\[4pt]
r
\\[4pt]
s
\\[4pt]
t
\end{matrix}\)
|
\(\begin{matrix}
(\operatorname{d}\text{m})
(\operatorname{d}\text{n})
\\[4pt]
~\operatorname{d}\text{m}~
(\operatorname{d}\text{n})
\\[4pt]
(\operatorname{d}\text{m})
~\operatorname{d}\text{n}~
\\[4pt]
~\operatorname{d}\text{m}~
~\operatorname{d}\text{n}~
\end{matrix}\)
|
\(\begin{matrix}
\langle\operatorname{d}!\rangle
\\[4pt]
\langle\operatorname{d}\text{m}\rangle
\\[4pt]
\langle\operatorname{d}\text{n}\rangle
\\[4pt]
\langle\operatorname{d}*\rangle
\end{matrix}\)
|
\(\begin{matrix}
\operatorname{d}!
\\[4pt]
\operatorname{d}\text{m}!
\\[4pt]
\operatorname{d}\text{n}!
\\[4pt]
\operatorname{d}*
\end{matrix}\)
|
\(\begin{matrix}
1
\\[4pt]
\operatorname{d}_{\text{m}}
\\[4pt]
\operatorname{d}_{\text{n}}
\\[4pt]
\operatorname{d}_{\text{m}} * \operatorname{d}_{\text{n}}
\end{matrix}\)
|
\(\text{Table 71.2} ~~ \text{Cosets of} ~ G_\text{m} ~ \text{in} ~ G\!\)
| \(\text{Group Coset}\!\)
|
\(\text{Logical Coset}\!\)
|
\(\text{Logical Element}\!\)
|
\(\text{Group Element}\!\)
| | \(G_\text{m}\!\)
|
\((\operatorname{d}\text{m})\!\)
|
\(\begin{matrix}
(\operatorname{d}\text{m})(\operatorname{d}\text{n})
\\[4pt]
(\operatorname{d}\text{m})~\operatorname{d}\text{n}~
\end{matrix}\)
|
\(\begin{matrix}
1
\\[4pt]
\operatorname{d}_\text{n}
\end{matrix}\)
| | \(G_\text{m} * \operatorname{d}_\text{m}\!\)
|
\(\operatorname{d}\text{m}\!\)
|
\(\begin{matrix}
~\operatorname{d}\text{m}~(\operatorname{d}\text{n})
\\[4pt]
~\operatorname{d}\text{m}~~\operatorname{d}\text{n}~
\end{matrix}\)
|
\(\begin{matrix}
\operatorname{d}_\text{m}
\\[4pt]
\operatorname{d}_\text{n} * \operatorname{d}_\text{m}
\end{matrix}\)
|
\(\text{Table 71.3} ~~ \text{Cosets of} ~ G_\text{n} ~ \text{in} ~ G\!\)
| \(\text{Group Coset}\!\)
|
\(\text{Logical Coset}\!\)
|
\(\text{Logical Element}\!\)
|
\(\text{Group Element}\!\)
| | \(G_\text{n}\!\)
|
\((\operatorname{d}\text{n})\!\)
|
\(\begin{matrix}
(\operatorname{d}\text{m})(\operatorname{d}\text{n})
\\[4pt]
~\operatorname{d}\text{m}~(\operatorname{d}\text{n})
\end{matrix}\)
|
\(\begin{matrix}
1
\\[4pt]
\operatorname{d}_\text{m}
\end{matrix}\)
| | \(G_\text{n} * \operatorname{d}_\text{n}\!\)
|
\(\operatorname{d}\text{n}\!\)
|
\(\begin{matrix}
(\operatorname{d}\text{m})~\operatorname{d}\text{n}~
\\[4pt]
~\operatorname{d}\text{m}~~\operatorname{d}\text{n}~
\end{matrix}\)
|
\(\begin{matrix}
\operatorname{d}_\text{n}
\\[4pt]
\operatorname{d}_\text{m} * \operatorname{d}_\text{n}
\end{matrix}\)
|
\(\text{Table 72.1} ~~ \text{Sign Relation of Interpreter A}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\text{Table 72.2} ~~ \text{Dyadic Projection} ~ L(\text{A})_{OS}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\text{Table 72.3} ~~ \text{Dyadic Projection} ~ L(\text{A})_{OI}\!\)
| \(\text{Object}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\text{Table 72.4} ~~ \text{Dyadic Projection} ~ L(\text{A})_{SI}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\text{Table 73.1} ~~ \text{Sign Relation of Interpreter B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\text{Table 73.2} ~~ \text{Dyadic Projection} ~ L(\text{B})_{OS}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\text{Table 73.3} ~~ \text{Dyadic Projection} ~ L(\text{B})_{OI}\!\)
| \(\text{Object}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\text{Table 73.4} ~~ \text{Dyadic Projection} ~ L(\text{B})_{SI}\!\)
| \(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
\end{matrix}\)
|
\(\text{Table 74.1} ~~ \text{Relation} ~ L_0 =\{ (x, y, z) \in \mathbb{B}^3 : x + y + z = 0 \}\!\)
| \(x\!\)
|
\(y\!\)
|
\(z\!\)
| | \(\begin{matrix}0\\0\\1\\1\end{matrix}\)
|
\(\begin{matrix}0\\1\\0\\1\end{matrix}\)
|
\(\begin{matrix}0\\1\\1\\0\end{matrix}\)
|
\(\text{Table 74.2} ~~ \text{Dyadic Projection} ~ (L_0)_{12}\!\)
| \(x\!\)
|
\(y\!\)
| | \(\begin{matrix}0\\0\\1\\1\end{matrix}\)
|
\(\begin{matrix}0\\1\\0\\1\end{matrix}\)
|
\(\text{Table 74.3} ~~ \text{Dyadic Projection} ~ (L_0)_{13}\!\)
| \(x\!\)
|
\(z\!\)
| | \(\begin{matrix}0\\0\\1\\1\end{matrix}\)
|
\(\begin{matrix}0\\1\\1\\0\end{matrix}\)
|
\(\text{Table 74.4} ~~ \text{Dyadic Projection} ~ (L_0)_{23}\!\)
| \(y\!\)
|
\(z\!\)
| | \(\begin{matrix}0\\1\\0\\1\end{matrix}\)
|
\(\begin{matrix}0\\1\\1\\0\end{matrix}\)
|
\(\text{Table 75.1} ~~ \text{Relation} ~ L_1 =\{ (x, y, z) \in \mathbb{B}^3 : x + y + z = 1 \}\!\)
| \(x\!\)
|
\(y\!\)
|
\(z\!\)
| | \(\begin{matrix}0\\0\\1\\1\end{matrix}\)
|
\(\begin{matrix}0\\1\\0\\1\end{matrix}\)
|
\(\begin{matrix}1\\0\\0\\1\end{matrix}\)
|
\(\text{Table 75.2} ~~ \text{Dyadic Projection} ~ (L_1)_{12}\!\)
| \(x\!\)
|
\(y\!\)
| | \(\begin{matrix}0\\0\\1\\1\end{matrix}\)
|
\(\begin{matrix}0\\1\\0\\1\end{matrix}\)
|
\(\text{Table 75.3} ~~ \text{Dyadic Projection} ~ (L_1)_{13}\!\)
| \(x\!\)
|
\(z\!\)
| | \(\begin{matrix}0\\0\\1\\1\end{matrix}\)
|
\(\begin{matrix}1\\0\\0\\1\end{matrix}\)
|
\(\text{Table 75.4} ~~ \text{Dyadic Projection} ~ (L_1)_{23}\!\)
| \(y\!\)
|
\(z\!\)
| | \(\begin{matrix}0\\1\\0\\1\end{matrix}\)
|
\(\begin{matrix}1\\0\\0\\1\end{matrix}\)
|
\(\text{Table 76.} ~~ \text{Attributed Sign Relation for Interpreters A and B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}
\end{matrix}\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}
\end{matrix}\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}
\end{matrix}\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{A}}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{A}}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{A}}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{A}}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}}
\\
{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}}
\\
{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{A}}
\end{matrix}\)
|
\(\text{Table 77.} ~~ \text{Augmented Sign Relation for Interpreters A and B}\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime}
\\
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime}
\end{matrix}\)
|
\(\text{Table 80.} ~~ \text{Reflective Extension} ~ \operatorname{Ref}^1 (\text{A})\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
\end{matrix}\)
|
\(\text{Table 81.} ~~ \text{Reflective Extension} ~ \operatorname{Ref}^1 (\text{B})\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
\\
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
\end{matrix}\)
|
\(\text{Table 82.} ~~ \text{Reflective Extension} ~ \operatorname{Ref}^1 (\text{A} | E_1)\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 83.} ~~ \text{Reflective Extension} ~ \operatorname{Ref}^1 (\text{B} | E_1)\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\text{Table 84.} ~~ \text{Reflective Extension} ~ \operatorname{Ref}^1 (\text{A} | E_2)\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
\text{A}
\\
\text{B}
\\
\text{A}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
\text{A}
\\
\text{B}
\\
\text{A}
\\
\text{B}
\end{matrix}\)
|
\(\text{Table 85.} ~~ \text{Reflective Extension} ~ \operatorname{Ref}^1 (\text{B} | E_2)\!\)
| \(\text{Object}\!\)
|
\(\text{Sign}\!\)
|
\(\text{Interpretant}\!\)
| |
\(\begin{matrix}
\text{A}
\\
\text{A}
\\
\text{A}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\\
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
\text{B}
\\
\text{B}
\\
\text{B}
\\
\text{B}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\end{matrix}\)
| |
\(\begin{matrix}
{}^{\langle} \text{A} {}^{\rangle}
\\
{}^{\langle} \text{B} {}^{\rangle}
\\
{}^{\langle} \text{i} {}^{\rangle}
\\
{}^{\langle} \text{u} {}^{\rangle}
\end{matrix}\)
|
\(\begin{matrix}
\text{A}
\\
\text{B}
\\
\text{B}
\\
\text{A}
\end{matrix}\)
|
\(\begin{matrix}
\text{A}
\\
\text{B}
\\
\text{B}
\\
\text{A}
\end{matrix}\)
|
Current Work
The semiotic equivalence relation given by \(\operatorname{Con}^1 (L_\text{A})\!\) for interpreter \(\text{A}\!\) has the following semiotic equations.
|
|
\([ {}^{\langle} \text{A} {}^{\rangle} ]_\text{A}\!\)
|
\(=\!\)
|
\([ {}^{\langle} \text{i} {}^{\rangle} ]_\text{A}\!\)
|
|
\([ {}^{\langle} \text{B} {}^{\rangle} ]_\text{A}\!\)
|
\(=\!\)
|
\([ {}^{\langle} \text{u} {}^{\rangle} ]_\text{A}\!\)
| | or
|
\({}^{\langle} \text{A} {}^{\rangle}\!\)
|
\(=_\text{A}\!\)
|
\({}^{\langle} \text{i} {}^{\rangle}\!\)
|
|
\({}^{\langle} \text{B} {}^{\rangle}\!\)
|
\(=_\text{A}\!\)
|
\({}^{\langle} \text{u} {}^{\rangle}\!\)
|
These equations induce the following semiotic partition.
|
\(
\{
\{ {}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle} \},
\{ {}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle} \},
\{ {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \}
\}.\!
\)
|
The semiotic equivalence relation given by \(\operatorname{Con}^1 (L_\text{B})\!\) for interpreter \(\text{B}\!\) has the following semiotic equations.
|
|
\([ {}^{\langle} \text{A} {}^{\rangle} ]_\text{B}\!\)
|
\(=\!\)
|
\([ {}^{\langle} \text{u} {}^{\rangle} ]_\text{B}\!\)
|
|
\([ {}^{\langle} \text{B} {}^{\rangle} ]_\text{B}\!\)
|
\(=\!\)
|
\([ {}^{\langle} \text{i} {}^{\rangle} ]_\text{B}\!\)
| | or
|
\({}^{\langle} \text{A} {}^{\rangle}\!\)
|
\(=_\text{B}\!\)
|
\({}^{\langle} \text{u} {}^{\rangle}\!\)
|
|
\({}^{\langle} \text{B} {}^{\rangle}\!\)
|
\(=_\text{B}\!\)
|
\({}^{\langle} \text{i} {}^{\rangle}\!\)
|
These equations induce the following semiotic partition.
|
\(
\{
\{ {}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle} \},
\{ {}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle} \},
\{ {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \}
\}.\!
\)
|
Table 86. Confounded Sign Relation C
Object Sign Interpretant
A "A" "A"
A "A" "i"
A "A" "u"
A "i" "A"
A "i" "i"
A "u" "A"
A "u" "u"
B "B" "B"
B "B" "i"
B "B" "u"
B "i" "B"
B "i" "i"
B "u" "B"
B "u" "u"
Table 87. Disjointed Sign Relation D
Object Sign Interpretant
AA "A"A "A"A
AA "A"A "i"A
AA "i"A "A"A
AA "i"A "i"A
AB "A"B "A"B
AB "A"B "u"B
AB "u"B "A"B
AB "u"B "u"B
BA "B"A "B"A
BA "B"A "u"A
BA "u"A "B"A
BA "u"A "u"A
BB "B"B "B"B
BB "B"B "i"B
BB "i"B "B"B
BB "i"B "i"B
|