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Revision as of 19:43, 15 May 2013
, 19:43, 15 May 2013→6.43. Reflective Extensions: markup
It may be observed that <math>S\!</math> overlaps with <math>O\!</math>O in the set of first-order signs or second-order objects, <math>S^{(1)} = O^{(2)},\!</math> exemplifying the extent to which signs have become objects in the new sign relations.
It may be observed that <math>S\!</math> overlaps with <math>O\!</math>O in the set of first-order signs or second-order objects, <math>S^{(1)} = O^{(2)},\!</math> exemplifying the extent to which signs have become objects in the new sign relations.
To discuss how the denotative and connotative aspects of a sign related are affected by its reflective extension it is useful to introduce a few abbreviations. For each sign relation <math>L\!</math> in <math>\{ L(\text{A}), L(\text{B}) \}\!</math> the following operations may be defined.
To discuss how the denotative and connotative aspects of a sign related are affected by its reflective extension it is useful to introduce a few abbreviations. For each sign relation <math>L\!</math> in <math>\{ L_\text{A}, L_\text{B} \}\!</math> the following operations may be defined.
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
<li>In the parts added by reflective extension <math>\operatorname{Den}^1 (L_\text{A})\!</math> and <math>\operatorname{Den}^1 (L_\text{B})\!</math> both have arcs from <math>{}^{\langle} s {}^{\rangle}\!</math> to <math>s,\!</math> for each <math>s \in S^{(1)}.\!</math></li>
<li>In the parts added by reflective extension <math>\operatorname{Den}^1 (L_\text{A})\!</math> and <math>\operatorname{Den}^1 (L_\text{B})\!</math> both have arcs from <math>{}^{\langle} s {}^{\rangle}\!</math> to <math>s,\!</math> for each <math>s \in S^{(1)}.\!</math></li>
</ol>
</ol>
Taken as transition digraphs, <math>\operatorname{Den}^1 (L_\text{A})\!</math> and <math>\operatorname{Den}^1 (L_\text{B})\!</math> summarize the upshots, end results, or effective steps of computation that are involved in the respective evaluations of signs in <math>S\!</math> by <math>\operatorname{Ref}^1 (\text{A})\!</math> and <math>\operatorname{Ref}^1 (\text{B}).\!</math>
<pre>
<pre>
The connotative components Con1 (A) and Con1 (B) can be pictured as digraphs on the eight points of the syntactic domain S. The arcs are given as follows:
The connotative components Con1 (A) and Con1 (B) can be pictured as digraphs on the eight points of the syntactic domain S. The arcs are given as follows:
