Changes

In applying the equivalence class notation to a sign relation <math>L,\!</math> the definitions and examples considered so far cover only the case where the connotative component <math>L_{SI}\!</math> is a total equivalence relation on the whole syntactic domain <math>S.\!</math>  The next job is to adapt this usage to PERs.

In applying the equivalence class notation to a sign relation <math>L,\!</math> the definitions and examples considered so far cover only the case where the connotative component <math>L_{SI}\!</math> is a total equivalence relation on the whole syntactic domain <math>S.\!</math>  The next job is to adapt this usage to PERs.

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If <math>L\!</math> is a sign relation whose syntactic projection <math>L_{SI}\!</math> is a PER on <math>S\!</math> then we may still write <math>{}^{\backprime\backprime} [s]_L {}^{\prime\prime}\!</math> for the &ldquo;equivalence class of <math>s\!</math> under <math>L_{SI}\!</math>&rdquo;.  But now, <math>[s]_L\!</math> can be empty if <math>s\!</math> has no interpretant, that is, if <math>s\!</math> lies outside the &ldquo;adequately meaningful&rdquo; subset of the syntactic domain, where synonymy and equivalence of meaning are defined.  Otherwise, if <math>s\!</math> has an <math>i\!</math> then it also has an <math>o,\!</math> by the definition of <math>L_{SI}.\!</math> In this case, there is a triple <math>(o, s, i) \in L,\!</math> and it is permissible to let <math>[o]_L = [s]_L.\!</math>

If R is a sign relation whose syntactic projection RSI is a PER on S, then I still write "[s]R" for the "equivalence class of s under RSI".  But now, [s]R can be empty if s has no interpretant, that is, if s lies outside the "adequately meaningful" subset of the syntactic domain, where synonymy and equivalence of meaning are defined.  Otherwise, if s has an i then it also has an o, by the definition of RSI.  In this case, there is a triple <o, s, i> C R, and it is permissible to let [o]R = [s]R.

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===6.32. Partiality : Selective Operations===

===6.32. Partiality : Selective Operations===