Difference between revisions of "Directory talk:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6"
Jon Awbrey (talk | contribs) |
Jon Awbrey (talk | contribs) (→Fragments: move fragments to talk page) |
||
| Line 2: | Line 2: | ||
==Fragments== | ==Fragments== | ||
| + | |||
| + | ===6.19. Examples of Self-Reference=== | ||
| + | |||
| + | In previous work I developed a version of propositional calculus based on C.S. Peirce's ''existential graphs'' and implemented this calculus in computational form as a ''sentential calculus interpreter''. Taking this calculus as a point of departure, I devised a theory of ''differential extensions'' for propositional domains that can be used, figuratively speaking, to put universes of discourse “in motion”, in other words, to provide qualitative descriptions of processes taking place in logical spaces. See (Awbrey, 1989 and 1994) for an account of this calculus, documentation of its computer program, and a detailed treatment of differential extensions. | ||
| + | |||
| + | In previous work (Awbrey, 1989) I described a system of notation for propositional calculus based on C.S. Peirce's ''existential graphs'', documented a computer implementation of this formalism, and showed how to provide this calculus with a ''differential extension'' that can be used to describe changing universes of discourse. In subsequent work (Awbrey, 1994) the resulting system of ''differential logic'' was applied to give qualitative descriptions of change in discrete dynamical systems. This section draws on that earlier work, summarizing the conceptions that are needed to give logical representations of sign relations and recording a few changes of a minor nature in the typographical conventions used. | ||
| + | |||
| + | Abstractly, a domain of propositions is known by the axioms it satisfies. Concretely, one thinks of a proposition as applying to the objects it is true of. | ||
| + | |||
| + | Logically, a domain of properties or propositions is known by the axioms it is subject to. Concretely, a property or proposition is known by the things or situations it is true of. Typically, the signs of properties and propositions are called ''terms'' and ''sentences'', respectively. | ||
==Scrap Area== | ==Scrap Area== | ||
Revision as of 21:28, 20 November 2012
Discussion
Fragments
6.19. Examples of Self-Reference
In previous work I developed a version of propositional calculus based on C.S. Peirce's existential graphs and implemented this calculus in computational form as a sentential calculus interpreter. Taking this calculus as a point of departure, I devised a theory of differential extensions for propositional domains that can be used, figuratively speaking, to put universes of discourse “in motion”, in other words, to provide qualitative descriptions of processes taking place in logical spaces. See (Awbrey, 1989 and 1994) for an account of this calculus, documentation of its computer program, and a detailed treatment of differential extensions.
In previous work (Awbrey, 1989) I described a system of notation for propositional calculus based on C.S. Peirce's existential graphs, documented a computer implementation of this formalism, and showed how to provide this calculus with a differential extension that can be used to describe changing universes of discourse. In subsequent work (Awbrey, 1994) the resulting system of differential logic was applied to give qualitative descriptions of change in discrete dynamical systems. This section draws on that earlier work, summarizing the conceptions that are needed to give logical representations of sign relations and recording a few changes of a minor nature in the typographical conventions used.
Abstractly, a domain of propositions is known by the axioms it satisfies. Concretely, one thinks of a proposition as applying to the objects it is true of.
Logically, a domain of properties or propositions is known by the axioms it is subject to. Concretely, a property or proposition is known by the things or situations it is true of. Typically, the signs of properties and propositions are called terms and sentences, respectively.
Scrap Area
Edit Buffer
When it comes to the subject of systems theory, a particular POV is so widely propagated that it might as well be regarded as the established, received, or traditional POV. The POV in question says that there are dynamic systems and symbolic systems, and never the twain shall meet. I naturally intend to challenge this assumption, preferring to suggest that dynamic …
Table Scraps
Table 37.1 Sign Relational Schema C Object Sign Interpretant x "x" "x" "x" "x" "x"
Table 37.2 Sign Relational Schema D Object Sign Interpretant x "x" "x"
Table 37.3 Sign Relational Schema E Object Sign Interpretant "x" "x" "x"
Table 37.4 Sign Relational Schema D' Object Sign Interpretant x "x" "x" x "x" <x> x <x> "x" x <x> <x>
Work Area
Alternate Text
A semigroup consists of a nonempty set with an associative LOC on it. On formal occasions, a semigroup is introduced by means a formula like \(X = (X, *),\!\) interpreted to mean that a semigroup \(X\!\) is specified by giving two pieces of data, a nonempty set that conventionally, if somewhat ambiguously, goes under the same name \({}^{\backprime\backprime} X {}^{\prime\prime},\!\) plus an associative binary operation denoted by \({}^{\backprime\backprime} * {}^{\prime\prime}.\!\) In contexts where there is only one semigroup being discussed, or where the additional structure is otherwise understood, it is common practice to call the semigroup by the name of the underlying set. In contexts where more than one semigroup is formed on the same set, one may use notations like \(X_i = (X, *_i)\!\) to distinguish them.
Additive Presentation
Version 1
- The \(n^\text{th}\!\) multiple of an element \(x\!\) in a semigroup \(\underline{X} = (X, +, 0),\!\) for integer \(n > 0,\!\) is notated as \(nx\!\) and defined as follows. Proceeding recursively, for \(n = 1,\!\) let \(1x = x,\!\) and for \(n > 1,\!\) let \(nx = (n-1)x + x.\!\)
- The \(n^\text{th}\!\) multiple of \(x\!\) in a monoid \(\underline{X} = (X, +, 0),\!\) for integer \(n \ge 0,\!\) is defined the same way for \(n > 0,\!\) letting \(0x = 0\!\) when \(n = 0.\!\)
- The \(n^\text{th}\!\) multiple of \(x\!\) in a group \(\underline{X} = (X, +, 0),\!\) for any integer \(n,\!\) is defined the same way for \(n \ge 0,\!\) letting \(nx = (-n)(-x)\!\) for \(n < 0.\!\)
Version 2
- In a semigroup written additively, the \(n^\text{th}\!\) multiple of an element \(x\!\) is notated as \(nx\!\) and defined for every positive integer \(n\!\) in the following manner. Proceeding recursively, let \(1x = x\!\) and let \(nx = (n-1)x + x\!\) for all \(n > 1.\!\)
- In a monoid written additively, the multiple \(nx\!\) is defined for every non-negative integer \(n\!\) by letting \(0x = 0\!\) and proceeding the same way for \(n > 0.\!\)
- In a group written additively, the multiple \(nx\!\) is defined for every integer \(n\!\) by letting \(nx = (-n)(-x)\!\) for \(n < 0\!\) and proceeding the same way for \(n \ge 0.\!\)
Set Displays
|
\(\begin{smallmatrix} \text{A} & = & \{ & (\text{A}, {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{A} {}^{\prime\prime}), & \ldots, & (\text{A}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}) & , & (\text{B}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}), & \ldots, & (\text{B}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime}) & \} \\[10pt] \text{B} & = & \{ & (\text{A}, {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{A} {}^{\prime\prime}), & \ldots, & (\text{A}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime}) & , & (\text{B}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}), & \ldots, & (\text{B}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}) & \} \end{smallmatrix}\) |
|
\(\begin{array}{lllllll} \text{A} & = & \{ & (\text{A}, {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{A} {}^{\prime\prime}), & \ldots, & (\text{A}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}), & \\ & & & (\text{B}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}), & \ldots, & (\text{B}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime}) & \} \\[10pt] \text{B} & = & \{ & (\text{A}, {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{A} {}^{\prime\prime}), & \ldots, & (\text{A}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime}), & \\ & & & (\text{B}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}), & \ldots, & (\text{B}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}) & \} \end{array}\) |
|
\(\begin{array}{*{15}{c}} W & = & \{ & \text{A} & , & \text{B} & , & {}^{\backprime\backprime} \text{A} {}^{\prime\prime} & , & {}^{\backprime\backprime} \text{B} {}^{\prime\prime} & , & {}^{\backprime\backprime} \text{i} {}^{\prime\prime} & , & {}^{\backprime\backprime} \text{u} {}^{\prime\prime} & \} \\ & = & \{ & w_1 & , & w_2 & , & w_3 & , & w_4 & , & w_5 & , & w_6 & \} \end{array}\) |
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
| \(*\!\) | \(x_0\!\) | \(\cdots\!\) | \(x_j\!\) | \(\cdots\!\) |
| \(x_0\!\) | \(x_0 * x_0\!\) | \(\cdots\!\) | \(x_0 * x_j\!\) | \(\cdots\!\) |
| \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) |
| \(x_i\!\) | \(x_i * x_0\!\) | \(\cdots\!\) | \(x_i * x_j\!\) | \(\cdots\!\) |
| \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) |
| \(\text{Element}\!\) | \(\text{Function as Set of Ordered Pairs of Elements}\!\) | |||||
| \(x_0\!\) | \(\{\!\) | \((x_0 ~,~ x_0 * x_0),\!\) | \(\cdots\!\) | \((x_j ~,~ x_0 * x_j),\!\) | \(\cdots\!\) | \(\}\!\) |
| \(\cdots\!\) | \(\{\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\}\!\) |
| \(x_i\!\) | \(\{\!\) | \((x_0 ~,~ x_i * x_0),\!\) | \(\cdots\!\) | \((x_j ~,~ x_i * x_j),\!\) | \(\cdots\!\) | \(\}\!\) |
| \(\cdots\!\) | \(\{\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\}\!\) |
| \(\text{Element}\!\) | \(\text{Function as Set of Ordered Pairs of Elements}\!\) | |||||
| \(x_0\!\) | \(\{\!\) | \((x_0 ~,~ x_0 * x_0),\!\) | \(\cdots\!\) | \((x_j ~,~ x_j * x_0),\!\) | \(\cdots\!\) | \(\}\!\) |
| \(\cdots\!\) | \(\{\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\}\!\) |
| \(x_i\!\) | \(\{\!\) | \((x_0 ~,~ x_0 * x_i),\!\) | \(\cdots\!\) | \((x_j ~,~ x_j * x_i),\!\) | \(\cdots\!\) | \(\}\!\) |
| \(\cdots\!\) | \(\{\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\cdots\!\) | \(\}\!\) |
| \(\cdot\!\) | \(\operatorname{e}\) | \(\operatorname{f}\) | \(\operatorname{g}\) | \(\operatorname{h}\) |
| \(\operatorname{e}\) | \(\operatorname{e}\) | \(\operatorname{f}\) | \(\operatorname{g}\) | \(\operatorname{h}\) |
| \(\operatorname{f}\) | \(\operatorname{f}\) | \(\operatorname{e}\) | \(\operatorname{h}\) | \(\operatorname{g}\) |
| \(\operatorname{g}\) | \(\operatorname{g}\) | \(\operatorname{h}\) | \(\operatorname{e}\) | \(\operatorname{f}\) |
| \(\operatorname{h}\) | \(\operatorname{h}\) | \(\operatorname{g}\) | \(\operatorname{f}\) | \(\operatorname{e}\) |
| \(\text{Element}\!\) | \(\text{Function as Set of Ordered Pairs of Elements}\!\) | |||||
| \(\operatorname{e}\) | \(\{\!\) | \((\operatorname{e}, \operatorname{e}),\) | \((\operatorname{f}, \operatorname{f}),\) | \((\operatorname{g}, \operatorname{g}),\) | \((\operatorname{h}, \operatorname{h})\) | \(\}\!\) |
| \(\operatorname{f}\) | \(\{\!\) | \((\operatorname{e}, \operatorname{f}),\) | \((\operatorname{f}, \operatorname{e}),\) | \((\operatorname{g}, \operatorname{h}),\) | \((\operatorname{h}, \operatorname{g})\) | \(\}\!\) |
| \(\operatorname{g}\) | \(\{\!\) | \((\operatorname{e}, \operatorname{g}),\) | \((\operatorname{f}, \operatorname{h}),\) | \((\operatorname{g}, \operatorname{e}),\) | \((\operatorname{h}, \operatorname{f})\) | \(\}\!\) |
| \(\operatorname{h}\) | \(\{\!\) | \((\operatorname{e}, \operatorname{h}),\) | \((\operatorname{f}, \operatorname{g}),\) | \((\operatorname{g}, \operatorname{f}),\) | \((\operatorname{h}, \operatorname{e})\) | \(\}\!\) |
| \(\text{Element}\!\) | \(\text{Function as Set of Ordered Pairs of Symbols}\!\) | |||||
| \(\operatorname{e}\) | \(\{\!\) | \(({}^{\backprime\backprime}\text{e}{}^{\prime\prime}, {}^{\backprime\backprime}\text{e}{}^{\prime\prime}),\) | \(({}^{\backprime\backprime}\text{f}{}^{\prime\prime}, {}^{\backprime\backprime}\text{f}{}^{\prime\prime}),\) | \(({}^{\backprime\backprime}\text{g}{}^{\prime\prime}, {}^{\backprime\backprime}\text{g}{}^{\prime\prime}),\) | \(({}^{\backprime\backprime}\text{h}{}^{\prime\prime}, {}^{\backprime\backprime}\text{h}{}^{\prime\prime})\) | \(\}\!\) |
| \(\operatorname{f}\) | \(\{\!\) | \(({}^{\backprime\backprime}\text{e}{}^{\prime\prime}, {}^{\backprime\backprime}\text{f}{}^{\prime\prime}),\) | \(({}^{\backprime\backprime}\text{f}{}^{\prime\prime}, {}^{\backprime\backprime}\text{e}{}^{\prime\prime}),\) | \(({}^{\backprime\backprime}\text{g}{}^{\prime\prime}, {}^{\backprime\backprime}\text{h}{}^{\prime\prime}),\) | \(({}^{\backprime\backprime}\text{h}{}^{\prime\prime}, {}^{\backprime\backprime}\text{g}{}^{\prime\prime})\) | \(\}\!\) |
| \(\operatorname{g}\) | \(\{\!\) | \(({}^{\backprime\backprime}\text{e}{}^{\prime\prime}, {}^{\backprime\backprime}\text{g}{}^{\prime\prime}),\) | \(({}^{\backprime\backprime}\text{f}{}^{\prime\prime}, {}^{\backprime\backprime}\text{h}{}^{\prime\prime}),\) | \(({}^{\backprime\backprime}\text{g}{}^{\prime\prime}, {}^{\backprime\backprime}\text{e}{}^{\prime\prime}),\) | \(({}^{\backprime\backprime}\text{h}{}^{\prime\prime}, {}^{\backprime\backprime}\text{f}{}^{\prime\prime})\) | \(\}\!\) |
| \(\operatorname{h}\) | \(\{\!\) | \(({}^{\backprime\backprime}\text{e}{}^{\prime\prime}, {}^{\backprime\backprime}\text{h}{}^{\prime\prime}),\) | \(({}^{\backprime\backprime}\text{f}{}^{\prime\prime}, {}^{\backprime\backprime}\text{g}{}^{\prime\prime}),\) | \(({}^{\backprime\backprime}\text{g}{}^{\prime\prime}, {}^{\backprime\backprime}\text{f}{}^{\prime\prime}),\) | \(({}^{\backprime\backprime}\text{h}{}^{\prime\prime}, {}^{\backprime\backprime}\text{e}{}^{\prime\prime})\) | \(\}\!\) |
| \(\cdot\!\) | \(\operatorname{1}\) | \(\operatorname{a}\) | \(\operatorname{b}\) | \(\operatorname{c}\) |
| \(\operatorname{1}\) | \(\operatorname{1}\) | \(\operatorname{a}\) | \(\operatorname{b}\) | \(\operatorname{c}\) |
| \(\operatorname{a}\) | \(\operatorname{a}\) | \(\operatorname{b}\) | \(\operatorname{c}\) | \(\operatorname{1}\) |
| \(\operatorname{b}\) | \(\operatorname{b}\) | \(\operatorname{c}\) | \(\operatorname{1}\) | \(\operatorname{a}\) |
| \(\operatorname{c}\) | \(\operatorname{c}\) | \(\operatorname{1}\) | \(\operatorname{a}\) | \(\operatorname{b}\) |
| \(\text{Element}\!\) | \(\text{Function as Set of Ordered Pairs of Elements}\!\) | |||||
| \(\operatorname{1}\) | \(\{\!\) | \((\operatorname{1}, \operatorname{1}),\) | \((\operatorname{a}, \operatorname{a}),\) | \((\operatorname{b}, \operatorname{b}),\) | \((\operatorname{c}, \operatorname{c})\) | \(\}\!\) |
| \(\operatorname{a}\) | \(\{\!\) | \((\operatorname{1}, \operatorname{a}),\) | \((\operatorname{a}, \operatorname{b}),\) | \((\operatorname{b}, \operatorname{c}),\) | \((\operatorname{c}, \operatorname{1})\) | \(\}\!\) |
| \(\operatorname{b}\) | \(\{\!\) | \((\operatorname{1}, \operatorname{b}),\) | \((\operatorname{a}, \operatorname{c}),\) | \((\operatorname{b}, \operatorname{1}),\) | \((\operatorname{c}, \operatorname{a})\) | \(\}\!\) |
| \(\operatorname{c}\) | \(\{\!\) | \((\operatorname{1}, \operatorname{c}),\) | \((\operatorname{a}, \operatorname{1}),\) | \((\operatorname{b}, \operatorname{a}),\) | \((\operatorname{c}, \operatorname{b})\) | \(\}\!\) |
| \(+\!\) | \(\operatorname{0}\) | \(\operatorname{1}\) | \(\operatorname{2}\) | \(\operatorname{3}\) |
| \(\operatorname{0}\) | \(\operatorname{0}\) | \(\operatorname{1}\) | \(\operatorname{2}\) | \(\operatorname{3}\) |
| \(\operatorname{1}\) | \(\operatorname{1}\) | \(\operatorname{2}\) | \(\operatorname{3}\) | \(\operatorname{0}\) |
| \(\operatorname{2}\) | \(\operatorname{2}\) | \(\operatorname{3}\) | \(\operatorname{0}\) | \(\operatorname{1}\) |
| \(\operatorname{3}\) | \(\operatorname{3}\) | \(\operatorname{0}\) | \(\operatorname{1}\) | \(\operatorname{2}\) |
| \(\text{Element}\!\) | \(\text{Function as Set of Ordered Pairs of Elements}\!\) | |||||
| \(\operatorname{0}\) | \(\{\!\) | \((\operatorname{0}, \operatorname{0}),\) | \((\operatorname{1}, \operatorname{1}),\) | \((\operatorname{2}, \operatorname{2}),\) | \((\operatorname{3}, \operatorname{3})\) | \(\}\!\) |
| \(\operatorname{1}\) | \(\{\!\) | \((\operatorname{0}, \operatorname{1}),\) | \((\operatorname{1}, \operatorname{2}),\) | \((\operatorname{2}, \operatorname{3}),\) | \((\operatorname{3}, \operatorname{0})\) | \(\}\!\) |
| \(\operatorname{2}\) | \(\{\!\) | \((\operatorname{0}, \operatorname{2}),\) | \((\operatorname{1}, \operatorname{3}),\) | \((\operatorname{2}, \operatorname{0}),\) | \((\operatorname{3}, \operatorname{1})\) | \(\}\!\) |
| \(\operatorname{3}\) | \(\{\!\) | \((\operatorname{0}, \operatorname{3}),\) | \((\operatorname{1}, \operatorname{0}),\) | \((\operatorname{2}, \operatorname{1}),\) | \((\operatorname{3}, \operatorname{2})\) | \(\}\!\) |
Sign Relations
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{A} \\ \text{A} \\ \text{A} \end{matrix}\) |
\(\begin{matrix} {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \end{matrix}\) |
|
\(\begin{matrix} \text{B} \\ \text{B} \\ \text{B} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{A} \\ \text{A} \\ \text{A} \end{matrix}\) |
\(\begin{matrix} {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
|
\(\begin{matrix} \text{B} \\ \text{B} \\ \text{B} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \end{matrix}\) |
| \(\text{Object Denoted}\!\) | \(\text{Equivalent Signs}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} & = & {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\ {}^{\langle} \text{B} {}^{\rangle} & = & {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \end{matrix}\) |
|
\(\begin{matrix} {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\ {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} {}^{\langle\langle} \text{A} {}^{\rangle\rangle} & = & {}^{\langle\backprime\backprime} \text{A} {}^{\prime\prime\rangle} & = & {}^{\backprime\backprime\langle} \text{A} {}^{\rangle\prime\prime} \\ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} & = & {}^{\langle\backprime\backprime} \text{B} {}^{\prime\prime\rangle} & = & {}^{\backprime\backprime\langle} \text{B} {}^{\rangle\prime\prime} \\ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} & = & {}^{\langle\backprime\backprime} \text{i} {}^{\prime\prime\rangle} & = & {}^{\backprime\backprime\langle} \text{i} {}^{\rangle\prime\prime} \\ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} & = & {}^{\langle\backprime\backprime} \text{u} {}^{\prime\prime\rangle} & = & {}^{\backprime\backprime\langle} \text{u} {}^{\rangle\prime\prime} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} \ldots \\[2pt] \ldots \\[2pt] \text{s} \end{matrix}\) |
\(\begin{matrix} \text{s} \\[2pt] \ldots \\[2pt] \text{t} \end{matrix}\) |
\(\begin{matrix} \ldots \\[2pt] \ldots \\[2pt] \ldots \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} x \\[2pt] {}^{\langle} x {}^{\rangle} \\[2pt] {}^{\langle\langle} x {}^{\rangle\rangle} \\[2pt] \ldots \end{matrix}\) |
\(\begin{matrix} {}^{\langle} x {}^{\rangle} \\[2pt] {}^{\langle\langle} x {}^{\rangle\rangle} \\[2pt] {}^{\langle\langle\langle} x {}^{\rangle\rangle\rangle} \\[2pt] \ldots \end{matrix}\) |
\(\begin{matrix} \ldots \\[2pt] \ldots \\[2pt] \ldots \\[2pt] \ldots \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} x \\[2pt] s_1 \\[2pt] s_2 \\[2pt] \ldots \end{matrix}\) |
\(\begin{matrix} s_1 \\[2pt] s_2 \\[2pt] s_3 \\[2pt] \ldots \end{matrix}\) |
\(\begin{matrix} \ldots \\[2pt] \ldots \\[2pt] \ldots \\[2pt] \ldots \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{A} \\ \text{A} \\ \text{A} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} \text{B} \\ \text{B} \\ \text{B} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{A} \\ \text{A} \\ \text{A} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} \text{B} \\ \text{B} \\ \text{B} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{A} \\ \text{A} \\ \text{A} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} \text{B} \\ \text{B} \\ \text{B} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \\ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \\ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \\ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \\ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \\ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \\ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{A} \\ \text{A} \\ \text{A} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} \text{B} \\ \text{B} \\ \text{B} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \\ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \\ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \\ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \\ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \\ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \\ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{A} \\ \text{A} \\ \text{A} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} \text{B} \\ \text{B} \\ \text{B} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{A} \\ \text{A} \\ \text{A} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} \text{B} \\ \text{B} \\ \text{B} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} L {}^{\rangle} \\ {}^{\langle} L {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} L {}^{\rangle} \\ {}^{\langle} L {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} q {}^{\rangle} \\ {}^{\langle} q {}^{\rangle} \\ {}^{\langle} q {}^{\rangle} \\ {}^{\langle} q {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} q {}^{\rangle} \\ {}^{\langle} q {}^{\rangle} \\ {}^{\langle} q {}^{\rangle} \\ {}^{\langle} q {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) \\ ( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) \\ ( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} (( & {}^{\langle} \text{A} {}^{\rangle} & , & \text{A} & ), & \text{A} & ) \\ (( & {}^{\langle} \text{A} {}^{\rangle} & , & \text{B} & ), & \text{A} & ) \\ (( & {}^{\langle} \text{B} {}^{\rangle} & , & \text{A} & ), & \text{B} & ) \\ (( & {}^{\langle} \text{B} {}^{\rangle} & , & \text{B} & ), & \text{B} & ) \\ (( & {}^{\langle} \text{i} {}^{\rangle} & , & \text{A} & ), & \text{A} & ) \\ (( & {}^{\langle} \text{i} {}^{\rangle} & , & \text{B} & ), & \text{B} & ) \\ (( & {}^{\langle} \text{u} {}^{\rangle} & , & \text{A} & ), & \text{B} & ) \\ (( & {}^{\langle} \text{u} {}^{\rangle} & , & \text{B} & ), & \text{A} & ) \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \\ {}^{\langle} \operatorname{De} {}^{\rangle} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{A} \\ \text{A} \\ \text{A} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} \text{B} \\ \text{B} \\ \text{B} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{A} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} ({}^{\langle} \text{A} {}^{\rangle}, \text{A}) \\ ({}^{\langle} \text{i} {}^{\rangle}, \text{A}) \end{matrix}\) |
|
\(\begin{matrix} \text{B} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} ({}^{\langle} \text{B} {}^{\rangle}, \text{B}) \\ ({}^{\langle} \text{u} {}^{\rangle}, \text{B}) \end{matrix}\) |
| \(\text{Sign}\!\) | \(\text{Interpretant}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} ({}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{A} {}^{\rangle}) \\ ({}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle}) \\ ({}^{\langle} \text{i} {}^{\rangle}, {}^{\langle} \text{A} {}^{\rangle}) \\ ({}^{\langle} \text{i} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle}) \end{matrix}\) |
|
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} ({}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{B} {}^{\rangle}) \\ ({}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle}) \\ ({}^{\langle} \text{u} {}^{\rangle}, {}^{\langle} \text{B} {}^{\rangle}) \\ ({}^{\langle} \text{u} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle}) \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{A} \\ \text{A} \\ \text{A} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
|
\(\begin{matrix} \text{B} \\ \text{B} \\ \text{B} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} \text{A} \\ \text{A} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} ({}^{\langle} \text{A} {}^{\rangle}, \text{A}) \\ ({}^{\langle} \text{u} {}^{\rangle}, \text{A}) \end{matrix}\) |
|
\(\begin{matrix} \text{B} \\ \text{B} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} ({}^{\langle} \text{B} {}^{\rangle}, \text{B}) \\ ({}^{\langle} \text{i} {}^{\rangle}, \text{B}) \end{matrix}\) |
| \(\text{Sign}\!\) | \(\text{Interpretant}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \\ {}^{\langle} \text{A} {}^{\rangle} \\ {}^{\langle} \text{u} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} ({}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{A} {}^{\rangle}) \\ ({}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle}) \\ ({}^{\langle} \text{u} {}^{\rangle}, {}^{\langle} \text{A} {}^{\rangle}) \\ ({}^{\langle} \text{u} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle}) \end{matrix}\) |
|
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \\ {}^{\langle} \text{B} {}^{\rangle} \\ {}^{\langle} \text{i} {}^{\rangle} \end{matrix}\) |
\(\begin{matrix} ({}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{B} {}^{\rangle}) \\ ({}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle}) \\ ({}^{\langle} \text{i} {}^{\rangle}, {}^{\langle} \text{B} {}^{\rangle}) \\ ({}^{\langle} \text{i} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle}) \end{matrix}\) |
Type Tables
| \(\text{Type}\!\) | \(\text{Symbol}\!\) |
|
\(\begin{array}{l} \text{Property} \\ \text{Sign} \\ \text{Set} \\ \text{Triple}\\ \text{Underlying Element} \end{array}\) |
\(\begin{matrix} P \\ \underline{S} \\ S \\ T \\ U \end{matrix}\) |
| \(\text{Type}\!\) | \(\text{Symbol}\!\) | \(\text{Construction}\!\) |
| \(\text{Relation}\!\) | \(R\!\) | \(S(T(U))\!\) |
| \(\text{Type}\!\) | \(\text{Symbol}\!\) | \(\text{Construction}\!\) |
| \(\text{Relation}\!\) | \(P(R)\!\) | \(P(S(T(U)))\!\) |
Completed Work
| \(\text{Object}\!\) | \(\text{Sign of Object}\!\) |
|
\(\begin{matrix} \text{A} & \text{A} & w_1 \\[6pt] \text{B} & \text{B} & w_2 \\[12pt] {}^{\backprime\backprime} \text{A} {}^{\prime\prime} & {}^{\langle} \text{A} {}^{\rangle} & w_3 \\[6pt] {}^{\backprime\backprime} \text{B} {}^{\prime\prime} & {}^{\langle} \text{B} {}^{\rangle} & w_4 \\[6pt] {}^{\backprime\backprime} \text{i} {}^{\prime\prime} & {}^{\langle} \text{i} {}^{\rangle} & w_5 \\[6pt] {}^{\backprime\backprime} \text{u} {}^{\prime\prime} & {}^{\langle} \text{u} {}^{\rangle} & w_6 \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \text{A} {}^{\rangle} & {}^{\langle} \text{A} {}^{\rangle} & {}^{\langle} w_1 {}^{\rangle} \\[6pt] {}^{\langle} \text{B} {}^{\rangle} & {}^{\langle} \text{B} {}^{\rangle} & {}^{\langle} w_2 {}^{\rangle} \\[12pt] {}^{\langle\backprime\backprime} \text{A} {}^{\prime\prime\rangle} & {}^{\langle\langle} \text{A} {}^{\rangle\rangle} & {}^{\langle} w_3 {}^{\rangle} \\[6pt] {}^{\langle\backprime\backprime} \text{B} {}^{\prime\prime\rangle} & {}^{\langle\langle} \text{B} {}^{\rangle\rangle} & {}^{\langle} w_4 {}^{\rangle} \\[6pt] {}^{\langle\backprime\backprime} \text{i} {}^{\prime\prime\rangle} & {}^{\langle\langle} \text{i} {}^{\rangle\rangle} & {}^{\langle} w_5 {}^{\rangle} \\[6pt] {}^{\langle\backprime\backprime} \text{u} {}^{\prime\prime\rangle} & {}^{\langle\langle} \text{u} {}^{\rangle\rangle} & {}^{\langle} w_6 {}^{\rangle} \end{matrix}\) |
| \(\text{Property}\!\) | \(\text{Sign of Property}\!\) |
|
\(\begin{matrix} {}^{\lbrace} \text{A} {}^{\rbrace} & {}^{\lbrace} \text{A} {}^{\rbrace} & {}^{\lbrace} w_1 {}^{\rbrace} \\[6pt] {}^{\lbrace} \text{B} {}^{\rbrace} & {}^{\lbrace} \text{B} {}^{\rbrace} & {}^{\lbrace} w_2 {}^{\rbrace} \\[12pt] {}^{\lbrace\backprime\backprime} \text{A} {}^{\prime\prime\rbrace} & {}^{\lbrace\langle} \text{A} {}^{\rangle\rbrace} & {}^{\lbrace} w_3 {}^{\rbrace} \\[6pt] {}^{\lbrace\backprime\backprime} \text{B} {}^{\prime\prime\rbrace} & {}^{\lbrace\langle} \text{B} {}^{\rangle\rbrace} & {}^{\lbrace} w_4 {}^{\rbrace} \\[6pt] {}^{\lbrace\backprime\backprime} \text{i} {}^{\prime\prime\rbrace} & {}^{\lbrace\langle} \text{i} {}^{\rangle\rbrace} & {}^{\lbrace} w_5 {}^{\rbrace} \\[6pt] {}^{\lbrace\backprime\backprime} \text{u} {}^{\prime\prime\rbrace} & {}^{\lbrace\langle} \text{u} {}^{\rangle\rbrace} & {}^{\lbrace} w_6 {}^{\rbrace} \end{matrix}\) |
\(\begin{matrix} {}^{\langle\lbrace} \text{A} {}^{\rbrace\rangle} & {}^{\langle\lbrace} \text{A} {}^{\rbrace\rangle} & {}^{\langle\lbrace} w_1 {}^{\rbrace\rangle} \\[6pt] {}^{\langle\lbrace} \text{B} {}^{\rbrace\rangle} & {}^{\langle\lbrace} \text{B} {}^{\rbrace\rangle} & {}^{\langle\lbrace} w_2 {}^{\rbrace\rangle} \\[12pt] {}^{\langle\lbrace\backprime\backprime} \text{A} {}^{\prime\prime\rbrace\rangle} & {}^{\langle\lbrace\langle} \text{A} {}^{\rangle\rbrace\rangle} & {}^{\langle\lbrace} w_3 {}^{\rbrace\rangle} \\[6pt] {}^{\langle\lbrace\backprime\backprime} \text{B} {}^{\prime\prime\rbrace\rangle} & {}^{\langle\lbrace\langle} \text{B} {}^{\rangle\rbrace\rangle} & {}^{\langle\lbrace} w_4 {}^{\rbrace\rangle} \\[6pt] {}^{\langle\lbrace\backprime\backprime} \text{i} {}^{\prime\prime\rbrace\rangle} & {}^{\langle\lbrace\langle} \text{i} {}^{\rangle\rbrace\rangle} & {}^{\langle\lbrace} w_5 {}^{\rbrace\rangle} \\[6pt] {}^{\langle\lbrace\backprime\backprime} \text{u} {}^{\prime\prime\rbrace\rangle} & {}^{\langle\lbrace\langle} \text{u} {}^{\rangle\rbrace\rangle} & {}^{\langle\lbrace} w_6 {}^{\rbrace\rangle} \end{matrix}\) |
| \(\text{Property}\!\) | \(\text{Sign of Property}\!\) |
|
\(\begin{matrix} \underline{\underline{\text{A}}} & \underline{\underline{\text{A}}} & \underline{\underline{w_1}} \\[6pt] \underline{\underline{\text{B}}} & \underline{\underline{\text{B}}} & \underline{\underline{w_2}} \\[12pt] \underline{\underline{{}^{\backprime\backprime} \text{A} {}^{\prime\prime}}} & \underline{\underline{{}^{\langle} \text{A} {}^{\rangle}}} & \underline{\underline{w_3}} \\[6pt] \underline{\underline{{}^{\backprime\backprime} \text{B} {}^{\prime\prime}}} & \underline{\underline{{}^{\langle} \text{B} {}^{\rangle}}} & \underline{\underline{w_4}} \\[6pt] \underline{\underline{{}^{\backprime\backprime} \text{i} {}^{\prime\prime}}} & \underline{\underline{{}^{\langle} \text{i} {}^{\rangle}}} & \underline{\underline{w_5}} \\[6pt] \underline{\underline{{}^{\backprime\backprime} \text{u} {}^{\prime\prime}}} & \underline{\underline{{}^{\langle} \text{u} {}^{\rangle}}} & \underline{\underline{w_6}} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \underline{\underline{\text{A}}} {}^{\rangle} & {}^{\langle} \underline{\underline{\text{A}}} {}^{\rangle} & {}^{\langle} \underline{\underline{w_1}} {}^{\rangle} \\[6pt] {}^{\langle} \underline{\underline{\text{B}}} {}^{\rangle} & {}^{\langle} \underline{\underline{\text{B}}} {}^{\rangle} & {}^{\langle} \underline{\underline{w_2}} {}^{\rangle} \\[12pt] {}^{\langle} \underline{\underline{{}^{\backprime\backprime} \text{A} {}^{\prime\prime}}} {}^{\rangle} & {}^{\langle} \underline{\underline{{}^{\langle} \text{A} {}^{\rangle}}} {}^{\rangle} & {}^{\langle} \underline{\underline{w_3}} {}^{\rangle} \\[6pt] {}^{\langle} \underline{\underline{{}^{\backprime\backprime} \text{B} {}^{\prime\prime}}} {}^{\rangle} & {}^{\langle} \underline{\underline{{}^{\langle} \text{B} {}^{\rangle}}} {}^{\rangle} & {}^{\langle} \underline{\underline{w_4}} {}^{\rangle} \\[6pt] {}^{\langle} \underline{\underline{{}^{\backprime\backprime} \text{i} {}^{\prime\prime}}} {}^{\rangle} & {}^{\langle} \underline{\underline{{}^{\langle} \text{i} {}^{\rangle}}} {}^{\rangle} & {}^{\langle} \underline{\underline{w_5}} {}^{\rangle} \\[6pt] {}^{\langle} \underline{\underline{{}^{\backprime\backprime} \text{u} {}^{\prime\prime}}} {}^{\rangle} & {}^{\langle} \underline{\underline{{}^{\langle} \text{u} {}^{\rangle}}} {}^{\rangle} & {}^{\langle} \underline{\underline{w_6}} {}^{\rangle} \end{matrix}\) |
| \(\text{Property}\!\) | \(\text{Sign of Property}\!\) |
|
\(\begin{matrix} \underline{\underline{\text{A}}} & \underline{\underline{o_1}} & \underline{\underline{w_1}} \\[6pt] \underline{\underline{\text{B}}} & \underline{\underline{o_2}} & \underline{\underline{w_2}} \\[12pt] \underline{\underline{\text{a}}} & \underline{\underline{s_1}} & \underline{\underline{w_3}} \\[6pt] \underline{\underline{\text{b}}} & \underline{\underline{s_2}} & \underline{\underline{w_4}} \\[6pt] \underline{\underline{\text{i}}} & \underline{\underline{s_3}} & \underline{\underline{w_5}} \\[6pt] \underline{\underline{\text{u}}} & \underline{\underline{s_4}} & \underline{\underline{w_6}} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \underline{\underline{\text{A}}} {}^{\rangle} & {}^{\langle} \underline{\underline{o_1}} {}^{\rangle} & {}^{\langle} \underline{\underline{w_1}} {}^{\rangle} \\[6pt] {}^{\langle} \underline{\underline{\text{B}}} {}^{\rangle} & {}^{\langle} \underline{\underline{o_2}} {}^{\rangle} & {}^{\langle} \underline{\underline{w_2}} {}^{\rangle} \\[12pt] {}^{\langle} \underline{\underline{\text{a}}} {}^{\rangle} & {}^{\langle} \underline{\underline{s_1}} {}^{\rangle} & {}^{\langle} \underline{\underline{w_3}} {}^{\rangle} \\[6pt] {}^{\langle} \underline{\underline{\text{b}}} {}^{\rangle} & {}^{\langle} \underline{\underline{s_2}} {}^{\rangle} & {}^{\langle} \underline{\underline{w_4}} {}^{\rangle} \\[6pt] {}^{\langle} \underline{\underline{\text{i}}} {}^{\rangle} & {}^{\langle} \underline{\underline{s_3}} {}^{\rangle} & {}^{\langle} \underline{\underline{w_5}} {}^{\rangle} \\[6pt] {}^{\langle} \underline{\underline{\text{u}}} {}^{\rangle} & {}^{\langle} \underline{\underline{s_4}} {}^{\rangle} & {}^{\langle} \underline{\underline{w_6}} {}^{\rangle} \end{matrix}\) |
| \(\text{Instance}\!\) | \(\text{Sign of Instance}\!\) |
|
\(\begin{matrix} {}^{\lbrack} \text{A} {}^{\rbrack} & {}^{\lbrack} \text{A} {}^{\rbrack} & {}^{\lbrack} w_1 {}^{\rbrack} \\[6pt] {}^{\lbrack} \text{B} {}^{\rbrack} & {}^{\lbrack} \text{B} {}^{\rbrack} & {}^{\lbrack} w_2 {}^{\rbrack} \\[12pt] {}^{\lbrack\backprime\backprime} \text{A} {}^{\prime\prime\rbrack} & {}^{\lbrack\langle} \text{A} {}^{\rangle\rbrack} & {}^{\lbrack} w_3 {}^{\rbrack} \\[6pt] {}^{\lbrack\backprime\backprime} \text{B} {}^{\prime\prime\rbrack} & {}^{\lbrack\langle} \text{B} {}^{\rangle\rbrack} & {}^{\lbrack} w_4 {}^{\rbrack} \\[6pt] {}^{\lbrack\backprime\backprime} \text{i} {}^{\prime\prime\rbrack} & {}^{\lbrack\langle} \text{i} {}^{\rangle\rbrack} & {}^{\lbrack} w_5 {}^{\rbrack} \\[6pt] {}^{\lbrack\backprime\backprime} \text{u} {}^{\prime\prime\rbrack} & {}^{\lbrack\langle} \text{u} {}^{\rangle\rbrack} & {}^{\lbrack} w_6 {}^{\rbrack} \end{matrix}\) |
\(\begin{matrix} {}^{\langle\lbrack} \text{A} {}^{\rbrack\rangle} & {}^{\langle\lbrack} \text{A} {}^{\rbrack\rangle} & {}^{\langle\lbrack} w_1 {}^{\rbrack\rangle} \\[6pt] {}^{\langle\lbrack} \text{B} {}^{\rbrack\rangle} & {}^{\langle\lbrack} \text{B} {}^{\rbrack\rangle} & {}^{\langle\lbrack} w_2 {}^{\rbrack\rangle} \\[12pt] {}^{\langle\lbrack\backprime\backprime} \text{A} {}^{\prime\prime\rbrack\rangle} & {}^{\langle\lbrack\langle} \text{A} {}^{\rangle\rbrack\rangle} & {}^{\langle\lbrack} w_3 {}^{\rbrack\rangle} \\[6pt] {}^{\langle\lbrack\backprime\backprime} \text{B} {}^{\prime\prime\rbrack\rangle} & {}^{\langle\lbrack\langle} \text{B} {}^{\rangle\rbrack\rangle} & {}^{\langle\lbrack} w_4 {}^{\rbrack\rangle} \\[6pt] {}^{\langle\lbrack\backprime\backprime} \text{i} {}^{\prime\prime\rbrack\rangle} & {}^{\langle\lbrack\langle} \text{i} {}^{\rangle\rbrack\rangle} & {}^{\langle\lbrack} w_5 {}^{\rbrack\rangle} \\[6pt] {}^{\langle\lbrack\backprime\backprime} \text{u} {}^{\prime\prime\rbrack\rangle} & {}^{\langle\lbrack\langle} \text{u} {}^{\rangle\rbrack\rangle} & {}^{\langle\lbrack} w_6 {}^{\rbrack\rangle} \end{matrix}\) |
| \(\text{Instance}\!\) | \(\text{Sign of Instance}\!\) |
|
\(\begin{matrix} \overline{\text{A}} & \overline{\text{A}} & \overline{w_1} \\[6pt] \overline{\text{B}} & \overline{\text{B}} & \overline{w_2} \\[12pt] \overline{{}^{\backprime\backprime} \text{A} {}^{\prime\prime}} & \overline{{}^{\langle} \text{A} {}^{\rangle}} & \overline{w_3} \\[6pt] \overline{{}^{\backprime\backprime} \text{B} {}^{\prime\prime}} & \overline{{}^{\langle} \text{B} {}^{\rangle}} & \overline{w_4} \\[6pt] \overline{{}^{\backprime\backprime} \text{i} {}^{\prime\prime}} & \overline{{}^{\langle} \text{i} {}^{\rangle}} & \overline{w_5} \\[6pt] \overline{{}^{\backprime\backprime} \text{u} {}^{\prime\prime}} & \overline{{}^{\langle} \text{u} {}^{\rangle}} & \overline{w_6} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \overline{\text{A}} {}^{\rangle} & {}^{\langle} \overline{\text{A}} {}^{\rangle} & {}^{\langle} \overline{w_1} {}^{\rangle} \\[6pt] {}^{\langle} \overline{\text{B}} {}^{\rangle} & {}^{\langle} \overline{\text{B}} {}^{\rangle} & {}^{\langle} \overline{w_2} {}^{\rangle} \\[12pt] {}^{\langle} \overline{{}^{\backprime\backprime} \text{A} {}^{\prime\prime}} {}^{\rangle} & {}^{\langle} \overline{{}^{\langle} \text{A} {}^{\rangle}} {}^{\rangle} & {}^{\langle} \overline{w_3} {}^{\rangle} \\[6pt] {}^{\langle} \overline{{}^{\backprime\backprime} \text{B} {}^{\prime\prime}} {}^{\rangle} & {}^{\langle} \overline{{}^{\langle} \text{B} {}^{\rangle}} {}^{\rangle} & {}^{\langle} \overline{w_4} {}^{\rangle} \\[6pt] {}^{\langle} \overline{{}^{\backprime\backprime} \text{i} {}^{\prime\prime}} {}^{\rangle} & {}^{\langle} \overline{{}^{\langle} \text{i} {}^{\rangle}} {}^{\rangle} & {}^{\langle} \overline{w_5} {}^{\rangle} \\[6pt] {}^{\langle} \overline{{}^{\backprime\backprime} \text{u} {}^{\prime\prime}} {}^{\rangle} & {}^{\langle} \overline{{}^{\langle} \text{u} {}^{\rangle}} {}^{\rangle} & {}^{\langle} \overline{w_6} {}^{\rangle} \end{matrix}\) |
| \(\text{Instance}\!\) | \(\text{Sign of Instance}\!\) |
|
\(\begin{matrix} \overline{\text{A}} & \overline{o_1} & \overline{w_1} \\[6pt] \overline{\text{B}} & \overline{o_2} & \overline{w_2} \\[12pt] \overline{\text{a}} & \overline{s_1} & \overline{w_3} \\[6pt] \overline{\text{b}} & \overline{s_2} & \overline{w_4} \\[6pt] \overline{\text{i}} & \overline{s_3} & \overline{w_5} \\[6pt] \overline{\text{u}} & \overline{s_4} & \overline{w_6} \end{matrix}\) |
\(\begin{matrix} {}^{\langle} \overline{\text{A}} {}^{\rangle} & {}^{\langle} \overline{o_1} {}^{\rangle} & {}^{\langle} \overline{w_1} {}^{\rangle} \\[6pt] {}^{\langle} \overline{\text{B}} {}^{\rangle} & {}^{\langle} \overline{o_2} {}^{\rangle} & {}^{\langle} \overline{w_2} {}^{\rangle} \\[12pt] {}^{\langle} \overline{\text{a}} {}^{\rangle} & {}^{\langle} \overline{s_1} {}^{\rangle} & {}^{\langle} \overline{w_3} {}^{\rangle} \\[6pt] {}^{\langle} \overline{\text{b}} {}^{\rangle} & {}^{\langle} \overline{s_2} {}^{\rangle} & {}^{\langle} \overline{w_4} {}^{\rangle} \\[6pt] {}^{\langle} \overline{\text{i}} {}^{\rangle} & {}^{\langle} \overline{s_3} {}^{\rangle} & {}^{\langle} \overline{w_5} {}^{\rangle} \\[6pt] {}^{\langle} \overline{\text{u}} {}^{\rangle} & {}^{\langle} \overline{s_4} {}^{\rangle} & {}^{\langle} \overline{w_6} {}^{\rangle} \end{matrix}\) |
| \(\text{Mnemonic Element}\!\) \(w \in W\!\) |
\(\text{Pragmatic Element}\!\) \(w \in W\!\) |
\(\text{Abstract Element}\!\) \(w_i \in W\!\) |
|
\(\begin{matrix} \text{A} \\[4pt] \text{B} \\[4pt] {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} o_1 \\[4pt] o_2 \\[4pt] s_1 \\[4pt] s_2 \\[4pt] s_3 \\[4pt] s_4 \end{matrix}\) |
\(\begin{matrix} w_1 \\[4pt] w_2 \\[4pt] w_3 \\[4pt] w_4 \\[4pt] w_5 \\[4pt] w_6 \end{matrix}\) |
|
\(\text{Mnemonic Feature}\!\) |
\(\text{Pragmatic Feature}\!\) |
\(\text{Abstract Feature}\!\) |
|
\(\begin{matrix} \underline{\underline{\text{A}}} \\[4pt] \underline{\underline{\text{B}}} \\[4pt] \underline{\underline{\text{a}}} \\[4pt] \underline{\underline{\text{b}}} \\[4pt] \underline{\underline{\text{i}}} \\[4pt] \underline{\underline{\text{u}}} \end{matrix}\) |
\(\begin{matrix} \underline{\underline{o_1}} \\[4pt] \underline{\underline{o_2}} \\[4pt] \underline{\underline{s_1}} \\[4pt] \underline{\underline{s_2}} \\[4pt] \underline{\underline{s_3}} \\[4pt] \underline{\underline{s_4}} \end{matrix}\) |
\(\begin{matrix} \underline{\underline{w_1}} \\[4pt] \underline{\underline{w_2}} \\[4pt] \underline{\underline{w_3}} \\[4pt] \underline{\underline{w_4}} \\[4pt] \underline{\underline{w_5}} \\[4pt] \underline{\underline{w_6}} \end{matrix}\) |
| \(\text{Element}\!\) | \(\text{Vector}\!\) | \(\text{Conjunct Term}\!\) | \(\text{Code}\!\) |
|
\(\begin{matrix} \text{A} \\[4pt] \text{B} \\[4pt] {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} 100000 \\[4pt] 010000 \\[4pt] 001000 \\[4pt] 000100 \\[4pt] 000010 \\[4pt] 000001 \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{A}}~ (\underline{\underline{B}}) (\underline{\underline{a}}) (\underline{\underline{b}}) (\underline{\underline{i}}) (\underline{\underline{u}}) \\[4pt] (\underline{\underline{A}}) ~\underline{\underline{B}}~ (\underline{\underline{a}}) (\underline{\underline{b}}) (\underline{\underline{i}}) (\underline{\underline{u}}) \\[4pt] (\underline{\underline{A}}) (\underline{\underline{B}}) ~\underline{\underline{a}}~ (\underline{\underline{b}}) (\underline{\underline{i}}) (\underline{\underline{u}}) \\[4pt] (\underline{\underline{A}}) (\underline{\underline{B}}) (\underline{\underline{a}}) ~\underline{\underline{b}}~ (\underline{\underline{i}}) (\underline{\underline{u}}) \\[4pt] (\underline{\underline{A}}) (\underline{\underline{B}}) (\underline{\underline{a}}) (\underline{\underline{b}}) ~\underline{\underline{i}}~ (\underline{\underline{u}}) \\[4pt] (\underline{\underline{A}}) (\underline{\underline{B}}) (\underline{\underline{a}}) (\underline{\underline{b}}) (\underline{\underline{i}}) ~\underline{\underline{u}}~ \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{A}}\rangle}_W \\[4pt] {\langle\underline{\underline{B}}\rangle}_W \\[4pt] {\langle\underline{\underline{a}}\rangle}_W \\[4pt] {\langle\underline{\underline{b}}\rangle}_W \\[4pt] {\langle\underline{\underline{i}}\rangle}_W \\[4pt] {\langle\underline{\underline{u}}\rangle}_W \end{matrix}\) |
| \(\text{Element}\!\) | \(\text{Vector}\!\) | \(\text{Conjunct Term}\!\) | \(\text{Code}\!\) |
|
\(\begin{matrix} \text{A} \\[4pt] \text{B} \\[4pt] {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} 100000 \\[4pt] 010000 \\[4pt] 001000 \\[4pt] 000100 \\[4pt] 000010 \\[4pt] 000001 \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{o_1}}~ (\underline{\underline{o_2}}) (\underline{\underline{s_1}}) (\underline{\underline{s_2}}) (\underline{\underline{s_3}}) (\underline{\underline{s_4}}) \\[4pt] (\underline{\underline{o_1}}) ~\underline{\underline{o_2}}~ (\underline{\underline{s_1}}) (\underline{\underline{s_2}}) (\underline{\underline{s_3}}) (\underline{\underline{s_4}}) \\[4pt] (\underline{\underline{o_1}}) (\underline{\underline{o_2}}) ~\underline{\underline{s_1}}~ (\underline{\underline{s_2}}) (\underline{\underline{s_3}}) (\underline{\underline{s_4}}) \\[4pt] (\underline{\underline{o_1}}) (\underline{\underline{o_2}}) (\underline{\underline{s_1}}) ~\underline{\underline{s_2}}~ (\underline{\underline{s_3}}) (\underline{\underline{s_4}}) \\[4pt] (\underline{\underline{o_1}}) (\underline{\underline{o_2}}) (\underline{\underline{s_1}}) (\underline{\underline{s_2}}) ~\underline{\underline{s_3}}~ (\underline{\underline{s_4}}) \\[4pt] (\underline{\underline{o_1}}) (\underline{\underline{o_2}}) (\underline{\underline{s_1}}) (\underline{\underline{s_2}}) (\underline{\underline{s_3}}) ~\underline{\underline{s_4}}~ \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{o_1}}\rangle}_W \\[4pt] {\langle\underline{\underline{o_2}}\rangle}_W \\[4pt] {\langle\underline{\underline{s_1}}\rangle}_W \\[4pt] {\langle\underline{\underline{s_2}}\rangle}_W \\[4pt] {\langle\underline{\underline{s_3}}\rangle}_W \\[4pt] {\langle\underline{\underline{s_4}}\rangle}_W \end{matrix}\) |
| \(\text{Element}\!\) | \(\text{Vector}\!\) | \(\text{Conjunct Term}\!\) | \(\text{Code}\!\) |
|
\(\begin{matrix} \text{A} \\[4pt] \text{B} \\[4pt] {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} 100000 \\[4pt] 010000 \\[4pt] 001000 \\[4pt] 000100 \\[4pt] 000010 \\[4pt] 000001 \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{w_1}}~ (\underline{\underline{w_2}}) (\underline{\underline{w_3}}) (\underline{\underline{w_4}}) (\underline{\underline{w_5}}) (\underline{\underline{w_6}}) \\[4pt] (\underline{\underline{w_1}}) ~\underline{\underline{w_2}}~ (\underline{\underline{w_3}}) (\underline{\underline{w_4}}) (\underline{\underline{w_5}}) (\underline{\underline{w_6}}) \\[4pt] (\underline{\underline{w_1}}) (\underline{\underline{w_2}}) ~\underline{\underline{w_3}}~ (\underline{\underline{w_4}}) (\underline{\underline{w_5}}) (\underline{\underline{w_6}}) \\[4pt] (\underline{\underline{w_1}}) (\underline{\underline{w_2}}) (\underline{\underline{w_3}}) ~\underline{\underline{w_4}}~ (\underline{\underline{w_5}}) (\underline{\underline{w_6}}) \\[4pt] (\underline{\underline{w_1}}) (\underline{\underline{w_2}}) (\underline{\underline{w_3}}) (\underline{\underline{w_4}}) ~\underline{\underline{w_5}}~ (\underline{\underline{w_6}}) \\[4pt] (\underline{\underline{w_1}}) (\underline{\underline{w_2}}) (\underline{\underline{w_3}}) (\underline{\underline{w_4}}) (\underline{\underline{w_5}}) ~\underline{\underline{w_6}}~ \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{w_1}}\rangle}_W \\[4pt] {\langle\underline{\underline{w_2}}\rangle}_W \\[4pt] {\langle\underline{\underline{w_3}}\rangle}_W \\[4pt] {\langle\underline{\underline{w_4}}\rangle}_W \\[4pt] {\langle\underline{\underline{w_5}}\rangle}_W \\[4pt] {\langle\underline{\underline{w_6}}\rangle}_W \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{A}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \end{matrix}\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{B}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{A}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} ({\langle\underline{\underline{\text{a}}}\rangle}_W, {\langle\underline{\underline{\text{A}}}\rangle}_W) \\[4pt] ({\langle\underline{\underline{\text{i}}}\rangle}_W, {\langle\underline{\underline{\text{A}}}\rangle}_W) \end{matrix}\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{B}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} ({\langle\underline{\underline{\text{b}}}\rangle}_W, {\langle\underline{\underline{\text{B}}}\rangle}_W) \\[4pt] ({\langle\underline{\underline{\text{u}}}\rangle}_W, {\langle\underline{\underline{\text{B}}}\rangle}_W) \end{matrix}\) |
| \(\text{Sign}\!\) | \(\text{Interpretant}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} 0_{\operatorname{d}W} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{a}}} ~ \operatorname{d}\underline{\underline{\text{i}}} \rangle}_{\operatorname{d}W} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{a}}} ~ \operatorname{d}\underline{\underline{\text{i}}} \rangle}_{\operatorname{d}W} \\[4pt] 0_{\operatorname{d}W} \end{matrix}\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} 0_{\operatorname{d}W} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{b}}} ~ \operatorname{d}\underline{\underline{\text{u}}} \rangle}_{\operatorname{d}W} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{b}}} ~ \operatorname{d}\underline{\underline{\text{u}}} \rangle}_{\operatorname{d}W} \\[4pt] 0_{\operatorname{d}W} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{A}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \end{matrix}\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{B}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{A}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} ({\langle\underline{\underline{\text{a}}}\rangle}_W, {\langle\underline{\underline{\text{A}}}\rangle}_W) \\[4pt] ({\langle\underline{\underline{\text{u}}}\rangle}_W, {\langle\underline{\underline{\text{A}}}\rangle}_W) \end{matrix}\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{B}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} ({\langle\underline{\underline{\text{b}}}\rangle}_W, {\langle\underline{\underline{\text{B}}}\rangle}_W) \\[4pt] ({\langle\underline{\underline{\text{i}}}\rangle}_W, {\langle\underline{\underline{\text{B}}}\rangle}_W) \end{matrix}\) |
| \(\text{Sign}\!\) | \(\text{Interpretant}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} 0_{\operatorname{d}W} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{a}}} ~ \operatorname{d}\underline{\underline{\text{u}}} \rangle}_{\operatorname{d}W} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{a}}} ~ \operatorname{d}\underline{\underline{\text{u}}} \rangle}_{\operatorname{d}W} \\[4pt] 0_{\operatorname{d}W} \end{matrix}\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_W \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_W \end{matrix}\) |
\(\begin{matrix} 0_{\operatorname{d}W} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{b}}} ~ \operatorname{d}\underline{\underline{\text{i}}} \rangle}_{\operatorname{d}W} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{b}}} ~ \operatorname{d}\underline{\underline{\text{i}}} \rangle}_{\operatorname{d}W} \\[4pt] 0_{\operatorname{d}W} \end{matrix}\) |
| \(\text{Element}\!\) | \(\text{Vector}\!\) | \(\text{Conjunct Term}\!\) | \(\text{Code}\!\) |
|
\(\begin{matrix} \text{A} \\[4pt] \text{B} \\[4pt] {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} {10}_X \\[4pt] {01}_X \\[4pt] {1000}_Y \\[4pt] {0100}_Y \\[4pt] {0010}_Y \\[4pt] {0001}_Y \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{A}}~ (\underline{\underline{B}}) \\[4pt] (\underline{\underline{A}}) ~\underline{\underline{B}}~ \\[4pt] ~\underline{\underline{a}}~ (\underline{\underline{b}}) (\underline{\underline{i}}) (\underline{\underline{u}}) \\[4pt] (\underline{\underline{a}}) ~\underline{\underline{b}}~ (\underline{\underline{i}}) (\underline{\underline{u}}) \\[4pt] (\underline{\underline{a}}) (\underline{\underline{b}}) ~\underline{\underline{i}}~ (\underline{\underline{u}}) \\[4pt] (\underline{\underline{a}}) (\underline{\underline{b}}) (\underline{\underline{i}}) ~\underline{\underline{u}}~ \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{A}}\rangle}_X \\[4pt] {\langle\underline{\underline{B}}\rangle}_X \\[4pt] {\langle\underline{\underline{a}}\rangle}_Y \\[4pt] {\langle\underline{\underline{b}}\rangle}_Y \\[4pt] {\langle\underline{\underline{i}}\rangle}_Y \\[4pt] {\langle\underline{\underline{u}}\rangle}_Y \end{matrix}\) |
| \(\text{Element}\!\) | \(\text{Vector}\!\) | \(\text{Conjunct Term}\!\) | \(\text{Code}\!\) |
|
\(\begin{matrix} \text{A} \\[4pt] \text{B} \\[4pt] {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} {10}_X \\[4pt] {01}_X \\[4pt] {1000}_Y \\[4pt] {0100}_Y \\[4pt] {0010}_Y \\[4pt] {0001}_Y \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{o_1}}~ (\underline{\underline{o_2}}) \\[4pt] (\underline{\underline{o_1}}) ~\underline{\underline{o_2}}~ \\[4pt] ~\underline{\underline{s_1}}~ (\underline{\underline{s_2}}) (\underline{\underline{s_3}}) (\underline{\underline{s_4}}) \\[4pt] (\underline{\underline{s_1}}) ~\underline{\underline{s_2}}~ (\underline{\underline{s_3}}) (\underline{\underline{s_4}}) \\[4pt] (\underline{\underline{s_1}}) (\underline{\underline{s_2}}) ~\underline{\underline{s_3}}~ (\underline{\underline{s_4}}) \\[4pt] (\underline{\underline{s_1}}) (\underline{\underline{s_2}}) (\underline{\underline{s_3}}) ~\underline{\underline{s_4}}~ \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{o_1}}\rangle}_X \\[4pt] {\langle\underline{\underline{o_2}}\rangle}_X \\[4pt] {\langle\underline{\underline{s_1}}\rangle}_Y \\[4pt] {\langle\underline{\underline{s_2}}\rangle}_Y \\[4pt] {\langle\underline{\underline{s_3}}\rangle}_Y \\[4pt] {\langle\underline{\underline{s_4}}\rangle}_Y \end{matrix}\) |
| \(\text{Element}\!\) | \(\text{Vector}\!\) | \(\text{Conjunct Term}\!\) | \(\text{Code}\!\) |
|
\(\begin{matrix} \text{A} \\[4pt] \text{B} \\[4pt] {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} {10}_X \\[4pt] {01}_X \\[4pt] {1000}_Y \\[4pt] {0100}_Y \\[4pt] {0010}_Y \\[4pt] {0001}_Y \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{x_1}}~ (\underline{\underline{x_2}}) \\[4pt] (\underline{\underline{x_1}}) ~\underline{\underline{x_2}}~ \\[4pt] ~\underline{\underline{y_1}}~ (\underline{\underline{y_2}}) (\underline{\underline{y_3}}) (\underline{\underline{y_4}}) \\[4pt] (\underline{\underline{y_1}}) ~\underline{\underline{y_2}}~ (\underline{\underline{y_3}}) (\underline{\underline{y_4}}) \\[4pt] (\underline{\underline{y_1}}) (\underline{\underline{y_2}}) ~\underline{\underline{y_3}}~ (\underline{\underline{y_4}}) \\[4pt] (\underline{\underline{y_1}}) (\underline{\underline{y_2}}) (\underline{\underline{y_3}}) ~\underline{\underline{y_4}}~ \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{x_1}}\rangle}_X \\[4pt] {\langle\underline{\underline{x_2}}\rangle}_X \\[4pt] {\langle\underline{\underline{y_1}}\rangle}_Y \\[4pt] {\langle\underline{\underline{y_2}}\rangle}_Y \\[4pt] {\langle\underline{\underline{y_3}}\rangle}_Y \\[4pt] {\langle\underline{\underline{y_4}}\rangle}_Y \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} ~\underline{\underline{\text{A}}}~ (\underline{\underline{\text{B}}}) \\[4pt] ~\underline{\underline{\text{A}}}~ (\underline{\underline{\text{B}}}) \\[4pt] ~\underline{\underline{\text{A}}}~ (\underline{\underline{\text{B}}}) \\[4pt] ~\underline{\underline{\text{A}}}~ (\underline{\underline{\text{B}}}) \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \\[4pt] ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \end{matrix}\) |
|
\(\begin{matrix} (\underline{\underline{\text{A}}}) ~\underline{\underline{\text{B}}}~ \\[4pt] (\underline{\underline{\text{A}}}) ~\underline{\underline{\text{B}}}~ \\[4pt] (\underline{\underline{\text{A}}}) ~\underline{\underline{\text{B}}}~ \\[4pt] (\underline{\underline{\text{A}}}) ~\underline{\underline{\text{B}}}~ \end{matrix}\) |
\(\begin{matrix} (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \end{matrix}\) |
\(\begin{matrix} (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \\[4pt] (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} ~\underline{\underline{\text{A}}}~ (\underline{\underline{\text{B}}}) \\[4pt] ~\underline{\underline{\text{A}}}~ (\underline{\underline{\text{B}}}) \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \end{matrix}\) |
\(\begin{matrix} ({\langle\underline{\underline{\text{a}}}\rangle}_Y, {\langle\underline{\underline{\text{A}}}\rangle}_X) \\[4pt] ({\langle\underline{\underline{\text{i}}}\rangle}_Y, {\langle\underline{\underline{\text{A}}}\rangle}_X) \end{matrix}\) |
|
\(\begin{matrix} (\underline{\underline{\text{A}}}) ~\underline{\underline{\text{B}}}~ \\[4pt] (\underline{\underline{\text{A}}}) ~\underline{\underline{\text{B}}}~ \end{matrix}\) |
\(\begin{matrix} (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \end{matrix}\) |
\(\begin{matrix} ({\langle\underline{\underline{\text{b}}}\rangle}_Y, {\langle\underline{\underline{\text{B}}}\rangle}_X) \\[4pt] ({\langle\underline{\underline{\text{u}}}\rangle}_Y, {\langle\underline{\underline{\text{B}}}\rangle}_X) \end{matrix}\) |
| \(\text{Sign}\!\) | \(\text{Interpretant}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \\[4pt] ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \end{matrix}\) |
\(\begin{matrix} (\underline{\underline{\text{da}}}) (\underline{\underline{\text{db}}}) (\underline{\underline{\text{di}}}) (\underline{\underline{\text{du}}}) \\[4pt] ~\underline{\underline{\text{da}}}~ (\underline{\underline{\text{db}}}) ~\underline{\underline{\text{di}}}~ (\underline{\underline{\text{du}}}) \\[4pt] ~\underline{\underline{\text{da}}}~ (\underline{\underline{\text{db}}}) ~\underline{\underline{\text{di}}}~ (\underline{\underline{\text{du}}}) \\[4pt] (\underline{\underline{\text{da}}}) (\underline{\underline{\text{db}}}) (\underline{\underline{\text{di}}}) (\underline{\underline{\text{du}}}) \end{matrix}\) |
|
\(\begin{matrix} (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \end{matrix}\) |
\(\begin{matrix} (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \\[4pt] (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \end{matrix}\) |
\(\begin{matrix} (\underline{\underline{\text{da}}}) (\underline{\underline{\text{db}}}) (\underline{\underline{\text{di}}}) (\underline{\underline{\text{du}}}) \\[4pt] (\underline{\underline{\text{da}}}) ~\underline{\underline{\text{db}}}~ (\underline{\underline{\text{di}}}) ~\underline{\underline{\text{du}}}~ \\[4pt] (\underline{\underline{\text{da}}}) ~\underline{\underline{\text{db}}}~ (\underline{\underline{\text{di}}}) ~\underline{\underline{\text{du}}}~ \\[4pt] (\underline{\underline{\text{da}}}) (\underline{\underline{\text{db}}}) (\underline{\underline{\text{di}}}) (\underline{\underline{\text{du}}}) \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} ~\underline{\underline{\text{A}}}~ (\underline{\underline{\text{B}}}) \\[4pt] ~\underline{\underline{\text{A}}}~ (\underline{\underline{\text{B}}}) \\[4pt] ~\underline{\underline{\text{A}}}~ (\underline{\underline{\text{B}}}) \\[4pt] ~\underline{\underline{\text{A}}}~ (\underline{\underline{\text{B}}}) \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \\[4pt] ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \end{matrix}\) |
|
\(\begin{matrix} (\underline{\underline{\text{A}}}) ~\underline{\underline{\text{B}}}~ \\[4pt] (\underline{\underline{\text{A}}}) ~\underline{\underline{\text{B}}}~ \\[4pt] (\underline{\underline{\text{A}}}) ~\underline{\underline{\text{B}}}~ \\[4pt] (\underline{\underline{\text{A}}}) ~\underline{\underline{\text{B}}}~ \end{matrix}\) |
\(\begin{matrix} (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \end{matrix}\) |
\(\begin{matrix} (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} ~\underline{\underline{\text{A}}}~ (\underline{\underline{\text{B}}}) \\[4pt] ~\underline{\underline{\text{A}}}~ (\underline{\underline{\text{B}}}) \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \end{matrix}\) |
\(\begin{matrix} ({\langle\underline{\underline{\text{a}}}\rangle}_Y, {\langle\underline{\underline{\text{A}}}\rangle}_X) \\[4pt] ({\langle\underline{\underline{\text{u}}}\rangle}_Y, {\langle\underline{\underline{\text{A}}}\rangle}_X) \end{matrix}\) |
|
\(\begin{matrix} (\underline{\underline{\text{A}}}) ~\underline{\underline{\text{B}}}~ \\[4pt] (\underline{\underline{\text{A}}}) ~\underline{\underline{\text{B}}}~ \end{matrix}\) |
\(\begin{matrix} (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \end{matrix}\) |
\(\begin{matrix} ({\langle\underline{\underline{\text{b}}}\rangle}_Y, {\langle\underline{\underline{\text{B}}}\rangle}_X) \\[4pt] ({\langle\underline{\underline{\text{i}}}\rangle}_Y, {\langle\underline{\underline{\text{B}}}\rangle}_X) \end{matrix}\) |
| \(\text{Sign}\!\) | \(\text{Interpretant}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \end{matrix}\) |
\(\begin{matrix} ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \\[4pt] ~\underline{\underline{\text{a}}}~ (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) (\underline{\underline{\text{i}}}) ~\underline{\underline{\text{u}}}~ \end{matrix}\) |
\(\begin{matrix} (\underline{\underline{\text{da}}}) (\underline{\underline{\text{db}}}) (\underline{\underline{\text{di}}}) (\underline{\underline{\text{du}}}) \\[4pt] ~\underline{\underline{\text{da}}}~ (\underline{\underline{\text{db}}}) (\underline{\underline{\text{di}}}) ~\underline{\underline{\text{du}}}~ \\[4pt] ~\underline{\underline{\text{da}}}~ (\underline{\underline{\text{db}}}) (\underline{\underline{\text{di}}}) ~\underline{\underline{\text{du}}}~ \\[4pt] (\underline{\underline{\text{da}}}) (\underline{\underline{\text{db}}}) (\underline{\underline{\text{di}}}) (\underline{\underline{\text{du}}}) \end{matrix}\) |
|
\(\begin{matrix} (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \end{matrix}\) |
\(\begin{matrix} (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) ~\underline{\underline{\text{b}}}~ (\underline{\underline{\text{i}}}) (\underline{\underline{\text{u}}}) \\[4pt] (\underline{\underline{\text{a}}}) (\underline{\underline{\text{b}}}) ~\underline{\underline{\text{i}}}~ (\underline{\underline{\text{u}}}) \end{matrix}\) |
\(\begin{matrix} (\underline{\underline{\text{da}}}) (\underline{\underline{\text{db}}}) (\underline{\underline{\text{di}}}) (\underline{\underline{\text{du}}}) \\[4pt] (\underline{\underline{\text{da}}}) ~\underline{\underline{\text{db}}}~ ~\underline{\underline{\text{di}}}~ (\underline{\underline{\text{du}}}) \\[4pt] (\underline{\underline{\text{da}}}) ~\underline{\underline{\text{db}}}~ ~\underline{\underline{\text{di}}}~ (\underline{\underline{\text{du}}}) \\[4pt] (\underline{\underline{\text{da}}}) (\underline{\underline{\text{db}}}) (\underline{\underline{\text{di}}}) (\underline{\underline{\text{du}}}) \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{A}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \end{matrix}\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{B}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{A}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} ({\langle\underline{\underline{\text{a}}}\rangle}_Y, {\langle\underline{\underline{\text{A}}}\rangle}_X) \\[4pt] ({\langle\underline{\underline{\text{i}}}\rangle}_Y, {\langle\underline{\underline{\text{A}}}\rangle}_X) \end{matrix}\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{B}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} ({\langle\underline{\underline{\text{b}}}\rangle}_Y, {\langle\underline{\underline{\text{B}}}\rangle}_X) \\[4pt] ({\langle\underline{\underline{\text{u}}}\rangle}_Y, {\langle\underline{\underline{\text{B}}}\rangle}_X) \end{matrix}\) |
| \(\text{Sign}\!\) | \(\text{Interpretant}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} 0_{\operatorname{d}Y} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{a}}} ~ \operatorname{d}\underline{\underline{\text{i}}} \rangle}_{\operatorname{d}Y} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{a}}} ~ \operatorname{d}\underline{\underline{\text{i}}} \rangle}_{\operatorname{d}Y} \\[4pt] 0_{\operatorname{d}Y} \end{matrix}\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} 0_{\operatorname{d}Y} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{b}}} ~ \operatorname{d}\underline{\underline{\text{u}}} \rangle}_{\operatorname{d}Y} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{b}}} ~ \operatorname{d}\underline{\underline{\text{u}}} \rangle}_{\operatorname{d}Y} \\[4pt] 0_{\operatorname{d}Y} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{A}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \end{matrix}\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{B}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{A}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{A}}}\rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} ({\langle\underline{\underline{\text{a}}}\rangle}_Y, {\langle\underline{\underline{\text{A}}}\rangle}_X) \\[4pt] ({\langle\underline{\underline{\text{u}}}\rangle}_Y, {\langle\underline{\underline{\text{A}}}\rangle}_X) \end{matrix}\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{B}}}\rangle}_X \\[4pt] {\langle\underline{\underline{\text{B}}}\rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} ({\langle\underline{\underline{\text{b}}}\rangle}_Y, {\langle\underline{\underline{\text{B}}}\rangle}_X) \\[4pt] ({\langle\underline{\underline{\text{i}}}\rangle}_Y, {\langle\underline{\underline{\text{B}}}\rangle}_X) \end{matrix}\) |
| \(\text{Sign}\!\) | \(\text{Interpretant}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{a}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{u}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} 0_{\operatorname{d}Y} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{a}}} ~ \operatorname{d}\underline{\underline{\text{u}}} \rangle}_{\operatorname{d}Y} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{a}}} ~ \operatorname{d}\underline{\underline{\text{u}}} \rangle}_{\operatorname{d}Y} \\[4pt] 0_{\operatorname{d}Y} \end{matrix}\) |
|
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{b}}}\rangle}_Y \\[4pt] {\langle\underline{\underline{\text{i}}}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} 0_{\operatorname{d}Y} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{b}}} ~ \operatorname{d}\underline{\underline{\text{i}}} \rangle}_{\operatorname{d}Y} \\[4pt] {\langle \operatorname{d}\underline{\underline{\text{b}}} ~ \operatorname{d}\underline{\underline{\text{i}}} \rangle}_{\operatorname{d}Y} \\[4pt] 0_{\operatorname{d}Y} \end{matrix}\) |
| \(\text{Category}\!\) | \(\text{Mnemonic}\!\) | \(\text{Code}\!\) |
|
\(\begin{array}{l} \text{Self} \\[4pt] \text{Other} \end{array}\) |
\(\begin{matrix} \text{self} \\[4pt] \text{(self)} \end{matrix}\) |
\(\begin{matrix} \text{s} \\[4pt] \text{(s)} \end{matrix}\) |
| \(\text{Category}\!\) | \(\text{Mnemonic}\!\) | \(\text{Code}\!\) |
|
\(\begin{array}{l} \text{1st Person} \\[4pt] \text{2nd Person} \end{array}\) |
\(\begin{matrix} \text{my} \\[4pt] \text{(my)} \end{matrix}\) |
\(\begin{matrix} \text{m} \\[4pt] \text{(m)} \end{matrix}\) |
| \(\text{Category}\!\) | \(\text{Mnemonic}\!\) | \(\text{Code}\!\) |
|
\(\begin{array}{l} \text{Noun} \\[4pt] \text{Pronoun} \end{array}\) |
\(\begin{matrix} \text{name} \\[4pt] \text{(name)} \end{matrix}\) |
\(\begin{matrix} \text{n} \\[4pt] \text{(n)} \end{matrix}\) |
| \(\text{Name}\!\) | \(\text{Vector}\!\) | \(\text{Conjunct Term}\!\) | \(\text{Mnemonic}\!\) | \(\text{Code}\!\) |
|
\(\begin{matrix} \text{A} \\[4pt] \text{B} \\[4pt] {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} {1}_X \\[4pt] {0}_X \\[4pt] {11}_Y \\[4pt] {01}_Y \\[4pt] {10}_Y \\[4pt] {00}_Y \end{matrix}\) |
\(\begin{matrix} ~x_1~ \\[4pt] (x_1) \\[4pt] ~y_1~~y_2~ \\[4pt] (y_1)~y_2~ \\[4pt] ~y_1~(y_2) \\[4pt] (y_1)(y_2) \end{matrix}\) |
\(\begin{matrix} ~\text{self}~ \\[4pt] (\text{self}) \\[4pt] ~\text{my}~~\text{name}~ \\[4pt] (\text{my})~\text{name}~ \\[4pt] ~\text{my}~(\text{name}) \\[4pt] (\text{my})(\text{name}) \end{matrix}\) |
\(\begin{matrix} ~\text{s}~ \\[4pt] (\text{s}) \\[4pt] ~\text{m}~~\text{n}~ \\[4pt] (\text{m})~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \\[4pt] (\text{m})(\text{n}) \end{matrix}\) |
| \(\text{Name}\!\) | \(\text{Vector}\!\) | \(\text{Conjunct Term}\!\) | \(\text{Mnemonic}\!\) | \(\text{Code}\!\) |
|
\(\begin{matrix} \text{A} \\[4pt] \text{B} \\[4pt] {}^{\backprime\backprime} \text{A} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{B} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \\[4pt] {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \end{matrix}\) |
\(\begin{matrix} {0}_X \\[4pt] {1}_X \\[4pt] {01}_Y \\[4pt] {11}_Y \\[4pt] {10}_Y \\[4pt] {00}_Y \end{matrix}\) |
\(\begin{matrix} (x_1) \\[4pt] ~x_1~ \\[4pt] (y_1)~y_2~ \\[4pt] ~y_1~~y_2~ \\[4pt] ~y_1~(y_2) \\[4pt] (y_1)(y_2) \end{matrix}\) |
\(\begin{matrix} (\text{self}) \\[4pt] ~\text{self}~ \\[4pt] (\text{my})~\text{name}~ \\[4pt] ~\text{my}~~\text{name}~ \\[4pt] ~\text{my}~(\text{name}) \\[4pt] (\text{my})(\text{name}) \end{matrix}\) |
\(\begin{matrix} (\text{s}) \\[4pt] ~\text{s}~ \\[4pt] (\text{m})~\text{n}~ \\[4pt] ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \\[4pt] (\text{m})(\text{n}) \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} \text{s} \\[4pt] \text{s} \\[4pt] \text{s} \\[4pt] \text{s} \end{matrix}\) |
\(\begin{matrix} ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \\[4pt] ~\text{m}~(\text{n}) \end{matrix}\) |
\(\begin{matrix} ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \\[4pt] ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \end{matrix}\) |
|
\(\begin{matrix} (\text{s}) \\[4pt] (\text{s}) \\[4pt] (\text{s}) \\[4pt] (\text{s}) \end{matrix}\) |
\(\begin{matrix} (\text{m})~\text{n}~ \\[4pt] (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \\[4pt] (\text{m})(\text{n}) \end{matrix}\) |
\(\begin{matrix} (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \\[4pt] (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} \text{s} \\[4pt] \text{s} \end{matrix}\) |
\(\begin{matrix} ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \end{matrix}\) |
\(\begin{matrix} ~\text{m}~~\text{n}~ \mapsto ~\text{s}~ \\[4pt] ~\text{m}~(\text{n}) \mapsto ~\text{s}~ \end{matrix}\) |
|
\(\begin{matrix} (\text{s}) \\[4pt] (\text{s}) \end{matrix}\) |
\(\begin{matrix} (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \end{matrix}\) |
\(\begin{matrix} (\text{m})~\text{n}~ \mapsto (\text{s}) \\[4pt] (\text{m})(\text{n}) \mapsto (\text{s}) \end{matrix}\) |
| \(\text{Sign}\!\) | \(\text{Interpretant}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \\[4pt] ~\text{m}~(\text{n}) \end{matrix}\) |
\(\begin{matrix} ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \\[4pt] ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \end{matrix}\) |
\(\begin{matrix} (\text{dm})(\text{dn}) \\[4pt] (\text{dm})~\text{dn}~ \\[4pt] (\text{dm})~\text{dn}~ \\[4pt] (\text{dm})(\text{dn}) \end{matrix}\) |
|
\(\begin{matrix} (\text{m})~\text{n}~ \\[4pt] (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \\[4pt] (\text{m})(\text{n}) \end{matrix}\) |
\(\begin{matrix} (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \\[4pt] (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \end{matrix}\) |
\(\begin{matrix} (\text{dm})(\text{dn}) \\[4pt] (\text{dm})~\text{dn}~ \\[4pt] (\text{dm})~\text{dn}~ \\[4pt] (\text{dm})(\text{dn}) \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} (\text{s}) \\[4pt] (\text{s}) \\[4pt] (\text{s}) \\[4pt] (\text{s}) \end{matrix}\) |
\(\begin{matrix} (\text{m})~\text{n}~ \\[4pt] (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \\[4pt] (\text{m})(\text{n}) \end{matrix}\) |
\(\begin{matrix} (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \\[4pt] (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \end{matrix}\) |
|
\(\begin{matrix} \text{s} \\[4pt] \text{s} \\[4pt] \text{s} \\[4pt] \text{s} \end{matrix}\) |
\(\begin{matrix} ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \\[4pt] ~\text{m}~(\text{n}) \end{matrix}\) |
\(\begin{matrix} ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \\[4pt] ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} (\text{s}) \\[4pt] (\text{s}) \end{matrix}\) |
\(\begin{matrix} (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \end{matrix}\) |
\(\begin{matrix} (\text{m})~\text{n}~ \mapsto (\text{s}) \\[4pt] (\text{m})(\text{n}) \mapsto (\text{s}) \end{matrix}\) |
|
\(\begin{matrix} \text{s} \\[4pt] \text{s} \end{matrix}\) |
\(\begin{matrix} ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \end{matrix}\) |
\(\begin{matrix} ~\text{m}~~\text{n}~ \mapsto ~\text{s}~ \\[4pt] ~\text{m}~(\text{n}) \mapsto ~\text{s}~ \end{matrix}\) |
| \(\text{Sign}\!\) | \(\text{Interpretant}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} (\text{m})~\text{n}~ \\[4pt] (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \\[4pt] (\text{m})(\text{n}) \end{matrix}\) |
\(\begin{matrix} (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \\[4pt] (\text{m})~\text{n}~ \\[4pt] (\text{m})(\text{n}) \end{matrix}\) |
\(\begin{matrix} (\text{dm})(\text{dn}) \\[4pt] (\text{dm})~\text{dn}~ \\[4pt] (\text{dm})~\text{dn}~ \\[4pt] (\text{dm})(\text{dn}) \end{matrix}\) |
|
\(\begin{matrix} ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \\[4pt] ~\text{m}~(\text{n}) \end{matrix}\) |
\(\begin{matrix} ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \\[4pt] ~\text{m}~~\text{n}~ \\[4pt] ~\text{m}~(\text{n}) \end{matrix}\) |
\(\begin{matrix} (\text{dm})(\text{dn}) \\[4pt] (\text{dm})~\text{dn}~ \\[4pt] (\text{dm})~\text{dn}~ \\[4pt] (\text{dm})(\text{dn}) \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} {\langle * \rangle}_X \\[4pt] {\langle * \rangle}_X \\[4pt] {\langle * \rangle}_X \\[4pt] {\langle * \rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle * \rangle}_Y \\[4pt] {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \\[4pt] {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \end{matrix}\) |
|
\(\begin{matrix} {\langle ! \rangle}_X \\[4pt] {\langle ! \rangle}_X \\[4pt] {\langle ! \rangle}_X \\[4pt] {\langle ! \rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle\text{n}\rangle}_Y \\[4pt] {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \\[4pt] {\langle ! \rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \\[4pt] {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {\langle * \rangle}_X \\[4pt] {\langle * \rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \end{matrix}\) |
\(\begin{array}{r} {\langle * \rangle}_Y \mapsto {\langle * \rangle}_X \\[4pt] {\langle\text{m}\rangle}_Y \mapsto {\langle * \rangle}_X \end{array}\) |
|
\(\begin{matrix} {\langle ! \rangle}_X \\[4pt] {\langle ! \rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \end{matrix}\) |
\(\begin{array}{r} {\langle\text{n}\rangle}_Y \mapsto {\langle ! \rangle}_X \\[4pt] {\langle ! \rangle}_Y \mapsto {\langle ! \rangle}_X \end{array}\) |
| \(\text{Sign}\!\) | \(\text{Interpretant}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {\langle * \rangle}_Y \\[4pt] {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \\[4pt] {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\operatorname{d}!\rangle}_{\operatorname{d}Y} \\[4pt] {\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y} \\[4pt] {\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y} \\[4pt] {\langle\operatorname{d}!\rangle}_{\operatorname{d}Y} \end{matrix}\) |
|
\(\begin{matrix} {\langle\text{n}\rangle}_Y \\[4pt] {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \\[4pt] {\langle ! \rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \\[4pt] {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\operatorname{d}!\rangle}_{\operatorname{d}Y} \\[4pt] {\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y} \\[4pt] {\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y} \\[4pt] {\langle\operatorname{d}!\rangle}_{\operatorname{d}Y} \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Interpretant}\!\) |
|
\(\begin{matrix} {\langle ! \rangle}_X \\[4pt] {\langle ! \rangle}_X \\[4pt] {\langle ! \rangle}_X \\[4pt] {\langle ! \rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle\text{n}\rangle}_Y \\[4pt] {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \\[4pt] {\langle ! \rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \\[4pt] {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \end{matrix}\) |
|
\(\begin{matrix} {\langle * \rangle}_X \\[4pt] {\langle * \rangle}_X \\[4pt] {\langle * \rangle}_X \\[4pt] {\langle * \rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle * \rangle}_Y \\[4pt] {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \\[4pt] {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \end{matrix}\) |
| \(\text{Object}\!\) | \(\text{Sign}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {\langle ! \rangle}_X \\[4pt] {\langle ! \rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \end{matrix}\) |
\(\begin{array}{r} {\langle\text{n}\rangle}_Y \mapsto {\langle ! \rangle}_X \\[4pt] {\langle ! \rangle}_Y \mapsto {\langle ! \rangle}_X \end{array}\) |
|
\(\begin{matrix} {\langle * \rangle}_X \\[4pt] {\langle * \rangle}_X \end{matrix}\) |
\(\begin{matrix} {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \end{matrix}\) |
\(\begin{array}{r} {\langle * \rangle}_Y \mapsto {\langle * \rangle}_X \\[4pt] {\langle\text{m}\rangle}_Y \mapsto {\langle * \rangle}_X \end{array}\) |
| \(\text{Sign}\!\) | \(\text{Interpretant}\!\) | \(\text{Transition}\!\) |
|
\(\begin{matrix} {\langle\text{n}\rangle}_Y \\[4pt] {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \\[4pt] {\langle ! \rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \\[4pt] {\langle\text{n}\rangle}_Y \\[4pt] {\langle ! \rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\operatorname{d}!\rangle}_{\operatorname{d}Y} \\[4pt] {\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y} \\[4pt] {\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y} \\[4pt] {\langle\operatorname{d}!\rangle}_{\operatorname{d}Y} \end{matrix}\) |
|
\(\begin{matrix} {\langle * \rangle}_Y \\[4pt] {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \\[4pt] {\langle * \rangle}_Y \\[4pt] {\langle\text{m}\rangle}_Y \end{matrix}\) |
\(\begin{matrix} {\langle\operatorname{d}!\rangle}_{\operatorname{d}Y} \\[4pt] {\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y} \\[4pt] {\langle\operatorname{d}\text{n}\rangle}_{\operatorname{d}Y} \\[4pt] {\langle\operatorname{d}!\rangle}_{\operatorname{d}Y} \end{matrix}\) |
| \(\text{Initial Premiss}\!\) | \(\text{Differential Premiss}\!\) | \(\text{Inferred Sequel}\!\) |
|
\(\begin{matrix} ~x~ ~\operatorname{at}~ t \\[4pt] ~x~ ~\operatorname{at}~ t \\[4pt] (x) ~\operatorname{at}~ t \\[4pt] (x) ~\operatorname{at}~ t \end{matrix}\) |
\(\begin{matrix} ~\operatorname{d}x~ ~\operatorname{at}~ t \\[4pt] (\operatorname{d}x) ~\operatorname{at}~ t \\[4pt] ~\operatorname{d}x~ ~\operatorname{at}~ t \\[4pt] (\operatorname{d}x) ~\operatorname{at}~ t \end{matrix}\) |
\(\begin{matrix} (x) ~\operatorname{at}~ t' \\[4pt] ~x~ ~\operatorname{at}~ t' \\[4pt] ~x~ ~\operatorname{at}~ t' \\[4pt] (x) ~\operatorname{at}~ t' \end{matrix}\) |
| \(\begin{matrix} \text{Abstract} \\ \text{Element} \end{matrix}\) | \(\begin{matrix} \text{Logical} \\ \text{Element} \end{matrix}\) | \(\begin{matrix} \text{Active} \\ \text{List} \end{matrix}\) | \(\begin{matrix} \text{Active} \\ \text{Term} \end{matrix}\) | \(\begin{matrix} \text{Genetic} \\ \text{Element} \end{matrix}\) |
|
\(\begin{matrix} 1 \\[4pt] r \\[4pt] s \\[4pt] t \end{matrix}\) |
\(\begin{matrix} (\operatorname{d}\underline{\underline{\text{a}}}) (\operatorname{d}\underline{\underline{\text{b}}}) (\operatorname{d}\underline{\underline{\text{i}}}) (\operatorname{d}\underline{\underline{\text{u}}}) \\[4pt] ~\operatorname{d}\underline{\underline{\text{a}}}~ (\operatorname{d}\underline{\underline{\text{b}}}) ~\operatorname{d}\underline{\underline{\text{i}}}~ (\operatorname{d}\underline{\underline{\text{u}}}) \\[4pt] (\operatorname{d}\underline{\underline{\text{a}}}) ~\operatorname{d}\underline{\underline{\text{b}}}~ (\operatorname{d}\underline{\underline{\text{i}}}) ~\operatorname{d}\underline{\underline{\text{u}}}~ \\[4pt] ~\operatorname{d}\underline{\underline{\text{a}}}~ ~\operatorname{d}\underline{\underline{\text{b}}}~ ~\operatorname{d}\underline{\underline{\text{i}}}~ ~\operatorname{d}\underline{\underline{\text{u}}}~ \end{matrix}\) |
\(\begin{matrix} \langle \operatorname{d}! \rangle \\[4pt] \langle \operatorname{d}\underline{\underline{\text{a}}} ~ \operatorname{d}\underline{\underline{\text{i}}} \rangle \\[4pt] \langle \operatorname{d}\underline{\underline{\text{b}}} ~ \operatorname{d}\underline{\underline{\text{u}}} \rangle \\[4pt] \langle \operatorname{d}* \rangle \end{matrix}\) |
\(\begin{matrix} \operatorname{d}! \\[4pt] \operatorname{d}\underline{\underline{\text{a}}} \cdot \operatorname{d}\underline{\underline{\text{i}}} ~ ! \\[4pt] \operatorname{d}\underline{\underline{\text{b}}} \cdot \operatorname{d}\underline{\underline{\text{u}}} ~ ! \\[4pt] \operatorname{d}* \end{matrix}\) |
\(\begin{matrix} 1 \\[4pt] \operatorname{d}_{\text{ai}} \\[4pt] \operatorname{d}_{\text{bu}} \\[4pt] \operatorname{d}_{\text{ai}} * \operatorname{d}_{\text{bu}} \end{matrix}\) |
| \(\begin{matrix} \text{Abstract} \\ \text{Element} \end{matrix}\) | \(\begin{matrix} \text{Logical} \\ \text{Element} \end{matrix}\) | \(\begin{matrix} \text{Active} \\ \text{List} \end{matrix}\) | \(\begin{matrix} \text{Active} \\ \text{Term} \end{matrix}\) | \(\begin{matrix} \text{Genetic} \\ \text{Element} \end{matrix}\) |
|
\(\begin{matrix} 1 \\[4pt] r \\[4pt] s \\[4pt] t \end{matrix}\) |
\(\begin{matrix} (\operatorname{d}\underline{\underline{\text{a}}}) (\operatorname{d}\underline{\underline{\text{b}}}) (\operatorname{d}\underline{\underline{\text{i}}}) (\operatorname{d}\underline{\underline{\text{u}}}) \\[4pt] ~\operatorname{d}\underline{\underline{\text{a}}}~ (\operatorname{d}\underline{\underline{\text{b}}}) (\operatorname{d}\underline{\underline{\text{i}}}) ~\operatorname{d}\underline{\underline{\text{u}}}~ \\[4pt] (\operatorname{d}\underline{\underline{\text{a}}}) ~\operatorname{d}\underline{\underline{\text{b}}}~ ~\operatorname{d}\underline{\underline{\text{i}}}~ (\operatorname{d}\underline{\underline{\text{u}}}) \\[4pt] ~\operatorname{d}\underline{\underline{\text{a}}}~ ~\operatorname{d}\underline{\underline{\text{b}}}~ ~\operatorname{d}\underline{\underline{\text{i}}}~ ~\operatorname{d}\underline{\underline{\text{u}}}~ \end{matrix}\) |
\(\begin{matrix} \langle \operatorname{d}! \rangle \\[4pt] \langle \operatorname{d}\underline{\underline{\text{a}}} ~ \operatorname{d}\underline{\underline{\text{u}}} \rangle \\[4pt] \langle \operatorname{d}\underline{\underline{\text{b}}} ~ \operatorname{d}\underline{\underline{\text{i}}} \rangle \\[4pt] \langle \operatorname{d}* \rangle \end{matrix}\) |
\(\begin{matrix} \operatorname{d}! \\[4pt] \operatorname{d}\underline{\underline{\text{a}}} \cdot \operatorname{d}\underline{\underline{\text{u}}} ~ ! \\[4pt] \operatorname{d}\underline{\underline{\text{b}}} \cdot \operatorname{d}\underline{\underline{\text{i}}} ~ ! \\[4pt] \operatorname{d}* \end{matrix}\) |
\(\begin{matrix} 1 \\[4pt] \operatorname{d}_{\text{au}} \\[4pt] \operatorname{d}_{\text{bi}} \\[4pt] \operatorname{d}_{\text{au}} * \operatorname{d}_{\text{bi}} \end{matrix}\) |
| \(\begin{matrix} \text{Abstract} \\ \text{Element} \end{matrix}\) | \(\begin{matrix} \text{Logical} \\ \text{Element} \end{matrix}\) | \(\begin{matrix} \text{Active} \\ \text{List} \end{matrix}\) | \(\begin{matrix} \text{Active} \\ \text{Term} \end{matrix}\) | \(\begin{matrix} \text{Genetic} \\ \text{Element} \end{matrix}\) |
|
\(\begin{matrix} 1 \\[4pt] r \\[4pt] s \\[4pt] t \end{matrix}\) |
\(\begin{matrix} (\operatorname{d}\text{m}) (\operatorname{d}\text{n}) \\[4pt] ~\operatorname{d}\text{m}~ (\operatorname{d}\text{n}) \\[4pt] (\operatorname{d}\text{m}) ~\operatorname{d}\text{n}~ \\[4pt] ~\operatorname{d}\text{m}~ ~\operatorname{d}\text{n}~ \end{matrix}\) |
\(\begin{matrix} \langle\operatorname{d}!\rangle \\[4pt] \langle\operatorname{d}\text{m}\rangle \\[4pt] \langle\operatorname{d}\text{n}\rangle \\[4pt] \langle\operatorname{d}*\rangle \end{matrix}\) |
\(\begin{matrix} \operatorname{d}! \\[4pt] \operatorname{d}\text{m}! \\[4pt] \operatorname{d}\text{n}! \\[4pt] \operatorname{d}* \end{matrix}\) |
\(\begin{matrix} 1 \\[4pt] \operatorname{d}_{\text{m}} \\[4pt] \operatorname{d}_{\text{n}} \\[4pt] \operatorname{d}_{\text{m}} * \operatorname{d}_{\text{n}} \end{matrix}\) |
| \(\begin{matrix} \text{Abstract} \\ \text{Element} \end{matrix}\) | \(\begin{matrix} \text{Logical} \\ \text{Element} \end{matrix}\) | \(\begin{matrix} \text{Active} \\ \text{List} \end{matrix}\) | \(\begin{matrix} \text{Active} \\ \text{Term} \end{matrix}\) | \(\begin{matrix} \text{Genetic} \\ \text{Element} \end{matrix}\) |
|
\(\begin{matrix} 1 \\[4pt] r \\[4pt] s \\[4pt] t \end{matrix}\) |
\(\begin{matrix} (\operatorname{d}\text{m}) (\operatorname{d}\text{n}) \\[4pt] ~\operatorname{d}\text{m}~ (\operatorname{d}\text{n}) \\[4pt] (\operatorname{d}\text{m}) ~\operatorname{d}\text{n}~ \\[4pt] ~\operatorname{d}\text{m}~ ~\operatorname{d}\text{n}~ \end{matrix}\) |
\(\begin{matrix} \langle\operatorname{d}!\rangle \\[4pt] \langle\operatorname{d}\text{m}\rangle \\[4pt] \langle\operatorname{d}\text{n}\rangle \\[4pt] \langle\operatorname{d}*\rangle \end{matrix}\) |
\(\begin{matrix} \operatorname{d}! \\[4pt] \operatorname{d}\text{m}! \\[4pt] \operatorname{d}\text{n}! \\[4pt] \operatorname{d}* \end{matrix}\) |
\(\begin{matrix} 1 \\[4pt] \operatorname{d}_{\text{m}} \\[4pt] \operatorname{d}_{\text{n}} \\[4pt] \operatorname{d}_{\text{m}} * \operatorname{d}_{\text{n}} \end{matrix}\) |
| \(\text{Group Coset}\!\) | \(\text{Logical Coset}\!\) | \(\text{Logical Element}\!\) | \(\text{Group Element}\!\) |
| \(G_\text{m}\!\) | \((\operatorname{d}\text{m})\!\) |
\(\begin{matrix} (\operatorname{d}\text{m})(\operatorname{d}\text{n}) \\[4pt] (\operatorname{d}\text{m})~\operatorname{d}\text{n}~ \end{matrix}\) |
\(\begin{matrix} 1 \\[4pt] \operatorname{d}_\text{n} \end{matrix}\) |
| \(G_\text{m} * \operatorname{d}_\text{m}\!\) | \(\operatorname{d}\text{m}\!\) |
\(\begin{matrix} ~\operatorname{d}\text{m}~(\operatorname{d}\text{n}) \\[4pt] ~\operatorname{d}\text{m}~~\operatorname{d}\text{n}~ \end{matrix}\) |
\(\begin{matrix} \operatorname{d}_\text{m} \\[4pt] \operatorname{d}_\text{n} * \operatorname{d}_\text{m} \end{matrix}\) |
| \(\text{Group Coset}\!\) | \(\text{Logical Coset}\!\) | \(\text{Logical Element}\!\) | \(\text{Group Element}\!\) |
| \(G_\text{n}\!\) | \((\operatorname{d}\text{n})\!\) |
\(\begin{matrix} (\operatorname{d}\text{m})(\operatorname{d}\text{n}) \\[4pt] ~\operatorname{d}\text{m}~(\operatorname{d}\text{n}) \end{matrix}\) |
\(\begin{matrix} 1 \\[4pt] \operatorname{d}_\text{m} \end{matrix}\) |
| \(G_\text{n} * \operatorname{d}_\text{n}\!\) | \(\operatorname{d}\text{n}\!\) |
\(\begin{matrix} (\operatorname{d}\text{m})~\operatorname{d}\text{n}~ \\[4pt] ~\operatorname{d}\text{m}~~\operatorname{d}\text{n}~ \end{matrix}\) |
\(\begin{matrix} \operatorname{d}_\text{n} \\[4pt] \operatorname{d}_\text{m} * \operatorname{d}_\text{n} \end{matrix}\) |
Current Work
