Changes

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These definitions for dyadic relations can now be applied in a context where each bit of a sign relation that is being considered satisfies a special set of conditions, namely, if <math>R\!</math> is the relation bit under consideration:

These definitions for dyadic relations can now be applied in a context where each bit of a sign relation that is being considered satisfies a special set of conditions, namely, if <math>R\!</math> is the relational bit under consideration:

# Syntactic domain X = Sign domain S = Interpretant domain I.

# Syntactic domain <math>X\!</math> = Sign domain <math>S\!</math> = Interpretant domain <math>I.\!</math>

# Connotative component = RXX = RSI = Equivalence relation E.

# Connotative component = <math>R_{XX}\!</math> = <math>R_{SI}\!</math> = Equivalence relation <math>E.\!</math>

Under these assumptions, and with regard to bits of sign relations that satisfy these conditions, it is useful to consider further selections of a specialized sort, namely, those that keep equivalent signs synonymous.

Under these assumptions, and with regard to bits of sign relations that satisfy these conditions, it is useful to consider further selections of a specialized sort, namely, those that keep equivalent signs synonymous.

An "arbit" of a sign relation is a slightly more judicious bit of it, preserving a semblance of whatever SEP happens to rule over its signs, and respecting the semiotic parts of the sampled sign relation, when it has such parts.  In other words, an arbit suggests an act of selection that represents the parts of the original SEP by means of the parts of the resulting SEP, that extracts an ISOS of each clique in the SER that it bothers to select any points at all from, and that manages to portray in at least this partial fashion all or none of every SEC that appears in the original sign relation.

An ''arbit'' of a sign relation is a slightly more judicious bit of it, preserving a semblance of whatever SEP happens to rule over its signs, and respecting the semiotic parts of the sampled sign relation, when it has such parts.  In other words, an arbit suggests an act of selection that represents the parts of the original SEP by means of the parts of the resulting SEP, that extracts an ISOS of each clique in the SER that it bothers to select any points at all from, and that manages to portray in at least this partial fashion all or none of every SEC that appears in the original sign relation.

=====1.3.10.3.  Propositions and Sentences=====

=====1.3.10.3.  Propositions and Sentences=====