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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 02:38, 18 May 2013
, 02:38, 18 May 2013→6.43. Reflective Extensions: markup
Taken as transition digraphs, <math>\operatorname{Con}^1 (L_\text{A})\!</math> and <math>\operatorname{Con}^1 (L_\text{B})\!</math> highlight the associations between signs in <math>\operatorname{Ref}^1 (L_\text{A})\!</math> and <math>\operatorname{Ref}^1 (L_\text{B}),\!</math> respectively.
Taken as transition digraphs, <math>\operatorname{Con}^1 (L_\text{A})\!</math> and <math>\operatorname{Con}^1 (L_\text{B})\!</math> highlight the associations between signs in <math>\operatorname{Ref}^1 (L_\text{A})\!</math> and <math>\operatorname{Ref}^1 (L_\text{B}),\!</math> respectively.
The semiotic equivalence relation given by <math>\operatorname{Con}^1 (L_\text{A})\!</math> for interpreter <math>\text{A}\!</math> has the following semiotic equations.
The SER given by Con1 (A) for interpreter A has the semantic equations:
[<A>]A = [<i>]A,
{| cellpadding="10"
| width="10%" |
| <math>[ {}^{\langle} \text{A} {}^{\rangle} ]_\text{A}\!</math>
| <math>=\!</math>
| <math>[ {}^{\langle} \text{i} {}^{\rangle} ]_\text{A}\!</math>
| width="20%" |
| <math>[ {}^{\langle} \text{B} {}^{\rangle} ]_\text{A}\!</math>
| <math>=\!</math>
| <math>[ {}^{\langle} \text{u} {}^{\rangle} ]_\text{A}\!</math>
|-
| width="10%" | or
| <math>{}^{\langle} \text{A} {}^{\rangle}\!</math>
| <math>=_\text{A}\!</math>
| <math>{}^{\langle} \text{i} {}^{\rangle}\!</math>
| width="20%" |
| <math>{}^{\langle} \text{B} {}^{\rangle}\!</math>
| <math>=_\text{A}\!</math>
| <math>{}^{\langle} \text{u} {}^{\rangle}\!</math>
|}
These equations induce the following semiotic partition.
{{ <A>, <i> }, { <<A>> }, { <<i>> },
{| align="center" cellspacing="6" width="90%"
|
<math>
\{
\{ {}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle} \},
\{ {}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle} \},
\{ {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \}
\}.\!
</math>
|}
The SER given by Con1 (B) for interpreter B has the semantic equations:
The semiotic equivalence relation given by <math>\operatorname{Con}^1 (L_\text{B})\!</math> for interpreter <math>\text{B}\!</math> has the following semiotic equations.
[<A>]B = [<u>]B,
{| cellpadding="10"
| width="10%" |
| <math>[ {}^{\langle} \text{A} {}^{\rangle} ]_\text{B}\!</math>
| <math>=\!</math>
| <math>[ {}^{\langle} \text{u} {}^{\rangle} ]_\text{B}\!</math>
| width="20%" |
| <math>[ {}^{\langle} \text{B} {}^{\rangle} ]_\text{B}\!</math>
| <math>=\!</math>
| <math>[ {}^{\langle} \text{i} {}^{\rangle} ]_\text{B}\!</math>
|-
| width="10%" | or
| <math>{}^{\langle} \text{A} {}^{\rangle}\!</math>
| <math>=_\text{B}\!</math>
| <math>{}^{\langle} \text{u} {}^{\rangle}\!</math>
| width="20%" |
| <math>{}^{\langle} \text{B} {}^{\rangle}\!</math>
| <math>=_\text{B}\!</math>
| <math>{}^{\langle} \text{i} {}^{\rangle}\!</math>
|}
These equations induce the following semiotic partition.
{{ <A>, <u> }, { <<A>> }, { <<u>> },
{| align="center" cellspacing="6" width="90%"
|
<math>
\{
\{ {}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle} \},
\{ {}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle} \},
\{ {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \}
\}.\!
</math>
|}
<pre>
Notice that the semantic equivalences of nouns and pronouns for each interpreter do not extend to equivalences of their second order signs, exactly as demanded by the literal character of quotations. Moreover, the new sign relations for A and B coincide in their reflective parts, since exactly the same triples were added to each set.
Notice that the semantic equivalences of nouns and pronouns for each interpreter do not extend to equivalences of their second order signs, exactly as demanded by the literal character of quotations. Moreover, the new sign relations for A and B coincide in their reflective parts, since exactly the same triples were added to each set.