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, 02:18, 16 May 2013
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| | ==Current Work== | | ==Current Work== |
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| − | The connotative components <math>\operatorname{Con}^1 (L_\text{A})\!</math> and <math>\operatorname{Con}^1 (L_\text{B})\!</math> can be viewed as digraphs on the eight points of the syntactic domain <math>S.\!</math> The arcs of these digraphs are given as follows.
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| − | <ol>
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| − | <li><math>\operatorname{Con}^1 (L_\text{A})\!</math> inherits from <math>L_\text{A}\!</math> the structure of a semiotic equivalence relation on <math>S^{(1)},\!</math> having a sling on each point of <math>S^{(1)},\!</math> arcs in both directions between <math>{}^{\langle} \text{A} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{i}{}^{\rangle},\!</math> and arcs in both directions between <math>{}^{\langle} \text{B} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{u}{}^{\rangle}.\!</math> The reflective extension <math>\operatorname{Ref}^1 (L_\text{A})\!</math> adds a sling on each point of <math>S^{(2)},\!</math> creating a semiotic equivalence relation on <math>S.\!</math></li>
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| − | <li><math>\operatorname{Con}^1 (L_\text{B})\!</math> inherits from <math>L_\text{B}\!</math> the structure of a semiotic equivalence relation on <math>S^{(1)},\!</math> having a sling on each point of <math>S^{(1)},\!</math> arcs in both directions between <math>{}^{\langle} \text{A} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{u}{}^{\rangle},\!</math> and arcs in both directions between <math>{}^{\langle} \text{B} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{i}{}^{\rangle}.\!</math> The reflective extension <math>\operatorname{Ref}^1 (L_\text{B})\!</math> adds a sling on each point of <math>S^{(2)},\!</math> creating a semiotic equivalence relation on <math>S.\!</math></li>
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| − | </ol>
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| − | 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.
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