Line 9,710:
Line 9,710:
<br>
<br>
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<pre>
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Thus informed, the semiotic equivalence relation for interpreter <math>\text{A}\!</math> yields the following semiotic equations.
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Thus informed, the SER for interpreter A yields the semantic equations:
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["A"A]A = ["A"B]A = ["i"A]A = ["u"B]A,
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{| cellpadding="10"
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| width="10%" |
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| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}]_\text{A}\!</math>
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| <math>=\!</math>
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| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}]_\text{A}\!</math>
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| <math>=\!</math>
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| <math>[{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}]_\text{A}\!</math>
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| <math>=\!</math>
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| <math>[{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}]_\text{A}\!</math>
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|-
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| width="10%" | or
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| <math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}\!</math>
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| <math>=_\text{A}\!</math>
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| <math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}\!</math>
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| <math>=_\text{A}\!</math>
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| <math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}\!</math>
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| <math>=_\text{A}\!</math>
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| <math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}\!</math>
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|}
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or "A"A =A "A"B =A "i"A =A "u"B.
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In comparison, the semiotic equivalence relation for interpreter <math>\text{B}\!</math> yields the following semiotic equations.
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In comparison, the SER for interpreter B yields the semantic equations:
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{| cellpadding="10"
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| width="10%" |
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["A"A]B = ["A"B]B = ["i"A]B = ["u"B]B,
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| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}]_\text{B}\!</math>
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| <math>=\!</math>
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or "A"A =B "A"B =B "i"A =B "u"B.
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| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}]_\text{B}\!</math>
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| <math>=\!</math>
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| <math>[{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}]_\text{B}\!</math>
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| <math>=\!</math>
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| <math>[{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}]_\text{B}\!</math>
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|-
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| width="10%" | or
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| <math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}\!</math>
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| <math>=_\text{B}\!</math>
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| <math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}\!</math>
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| <math>=_\text{B}\!</math>
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| <math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}\!</math>
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| <math>=_\text{B}\!</math>
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| <math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}\!</math>
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|}
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<pre>
Consequently, both SERs now induce the same semantic partition on S:
Consequently, both SERs now induce the same semantic partition on S: