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| | ==Current Work== | | ==Current Work== |
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| − | <br>
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| − | 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.
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| − | {| cellpadding="10"
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| − | | width="10%" |
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| − | | <math>[ {}^{\langle} \text{A} {}^{\rangle} ]_\text{A}\!</math>
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| − | | <math>=\!</math>
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| − | | <math>[ {}^{\langle} \text{i} {}^{\rangle} ]_\text{A}\!</math>
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| − | | width="20%" |
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| − | | <math>[ {}^{\langle} \text{B} {}^{\rangle} ]_\text{A}\!</math>
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| − | | <math>=\!</math>
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| − | | <math>[ {}^{\langle} \text{u} {}^{\rangle} ]_\text{A}\!</math>
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| − | |-
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| − | | width="10%" | or
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| − | | <math>{}^{\langle} \text{A} {}^{\rangle}\!</math>
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| − | | <math>=_\text{A}\!</math>
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| − | | <math>{}^{\langle} \text{i} {}^{\rangle}\!</math>
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| − | | width="20%" |
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| − | | <math>{}^{\langle} \text{B} {}^{\rangle}\!</math>
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| − | | <math>=_\text{A}\!</math>
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| − | | <math>{}^{\langle} \text{u} {}^{\rangle}\!</math>
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| − | |}
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| − | These equations induce the following semiotic partition.
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| − | {| align="center" cellspacing="6" width="90%"
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| − | <math>
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| − | \{
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| − | \{ {}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle} \},
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| − | \{ {}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle} \},
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| − | \{ {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \},
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| − | \{ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \},
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| − | \{ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \},
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| − | \{ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \}
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| − | \}.\!
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| − | </math>
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| − | |}
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| − | 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.
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| − |
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| − | {| cellpadding="10"
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| − | | width="10%" |
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| − | | <math>[ {}^{\langle} \text{A} {}^{\rangle} ]_\text{B}\!</math>
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| − | | <math>=\!</math>
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| − | | <math>[ {}^{\langle} \text{u} {}^{\rangle} ]_\text{B}\!</math>
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| − | | width="20%" |
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| − | | <math>[ {}^{\langle} \text{B} {}^{\rangle} ]_\text{B}\!</math>
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| − | | <math>=\!</math>
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| − | | <math>[ {}^{\langle} \text{i} {}^{\rangle} ]_\text{B}\!</math>
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| − | |-
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| − | | width="10%" | or
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| − | | <math>{}^{\langle} \text{A} {}^{\rangle}\!</math>
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| − | | <math>=_\text{B}\!</math>
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| − | | <math>{}^{\langle} \text{u} {}^{\rangle}\!</math>
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| − | | width="20%" |
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| − | | <math>{}^{\langle} \text{B} {}^{\rangle}\!</math>
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| − | | <math>=_\text{B}\!</math>
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| − | | <math>{}^{\langle} \text{i} {}^{\rangle}\!</math>
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| − | |}
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| − |
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| − | These equations induce the following semiotic partition.
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| − |
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| − | {| align="center" cellspacing="6" width="90%"
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| − | |
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| − | <math>
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| − | \{
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| − | \{ {}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle} \},
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| − | \{ {}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle} \},
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| − | \{ {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \},
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| − | \{ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \},
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| − | \{ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \},
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| − | \{ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \}
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| − | \}.\!
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| − | </math>
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| − | |}
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| | <br> | | <br> |