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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 17:18, 18 April 2013
, 17:18, 18 April 2013→6.38. Considering the Source: markup
S = { "[<A>]A", "[<B>]A", "[<i>]A", "[<u>]A",
S = { "[<A>]A", "[<B>]A", "[<i>]A", "[<u>]A",
"[<A>]B", "[<B>]B", "[<i>]B", "[<u>]B" }
"[<A>]B", "[<B>]B", "[<i>]B", "[<u>]B" }
</pre>
The situated sign or indexed expression "[<A>]B" presents the sign or expression "A" as used by the interpreter B. In other words, the sign is indexed by the name of an interpreter to indicate a use of that sign by that interpreter. Thus, "[<A>]B" augments "A" into a new and more complete sign by including additional information about the context of its transmission, in particular, by the consideration of its source.
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{ccl}
O & = &
\{ \text{A}, \text{B} \}
\\[6pt]
S & = &
\{
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
\}
\\[6pt]
I & = &
\{
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{A} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{B} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{i} {}^\rangle ]_\text{B} {}^{\prime\prime},
{}^{\backprime\backprime} [ {}^\langle \text{u} {}^\rangle ]_\text{B} {}^{\prime\prime}
\}
\end{array}</math>
|}
The situated sign or indexed expression <math>{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime}\!</math> presents the sign or expression <math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime}\!</math> as used by the interpreter <math>\text{B}.\!</math> In other words, the sign is indexed by the name of an interpreter to indicate a use of that sign by that interpreter. Thus, <math>{}^{\backprime\backprime} [ {}^\langle \text{A} {}^\rangle ]_\text{B} {}^{\prime\prime}\!</math> augments <math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime}\!</math> to form a new and more complete sign by including additional information about the context of its transmission, in particular, by the consideration of its source.
<br>
<br>
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
|+ style="height:30px" | <math>\text{Table 77.} ~~ \text{Adequated Sign Relation for Interpreters A and B}\!</math>
|+ style="height:30px" | <math>\text{Table 77.} ~~ \text{Augmented Sign Relation for Interpreters A and B}\!</math>
|- style="height:40px; background:#f0f0ff"
|- style="height:40px; background:#f0f0ff"
| width="33%" | <math>\text{Object}\!</math>
| width="33%" | <math>\text{Object}\!</math>