Changes

:: <math>\operatorname{Den}(\text{B})</math> has an arc from each point of <math>\{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \}</math> to <math>\text{A}</math> and from each point of <math>\{ {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \}</math> to <math>\text{B}</math>.

:: <math>\operatorname{Den}(\text{B})</math> has an arc from each point of <math>\{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \}</math> to <math>\text{A}</math> and from each point of <math>\{ {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \}</math> to <math>\text{B}</math>.

Den(''A'') and Den(''B'') can be interpreted as ''transition digraphs'' that chart the succession of steps or the connection of states in a computational process.  If the graph is read this way, the denotational arcs summarize the ''upshots'' of the computations that are involved when the interpreters ''A'' and ''B'' evaluate the signs in ''S'' according to their own frames of reference.

<math>\operatorname{Den}(\text{A})</math> and <math>\operatorname{Den}(\text{B})</math> can be interpreted as ''transition digraphs'' that chart the succession of steps or the connection of states in a computational process.  If the graphs are read this way, the denotational arcs summarize the ''upshots'' of the computations that are involved when the interpreters <math>\text{A}</math> and <math>\text{B}</math> evaluate the signs in <math>S</math> according to their own frames of reference.

The connotative components Con(''A'') and Con(''B'') can be represented as digraphs on the four points of their common syntactic domain ''S'' = ''I'' = {"''A''",&nbsp;"''B''",&nbsp;"''i''",&nbsp;"''u''"}.  Since Con(''A'') and Con(''B'') are SER's, their digraphs conform to the pattern that is manifested by all digraphs of equivalence relations.  In general, a digraph of an equivalence relation falls into connected components that correspond to the parts of the associated partition, with a complete digraph on the points of each part, and no other arcs.  In the present case, the arcs are given as follows:

The connotative components <math>\operatorname{Con}(\text{A})</math> and <math>\operatorname{Con}(\text{B})</math> can be represented as digraphs on the four points of their common syntactic domain <math>S = I = \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \}</math>.  Since <math>\operatorname{Con}(\text{A})</math> and <math>\operatorname{Con}(\text{B})</math> are SERs, their digraphs conform to the pattern that is manifested by all digraphs of equivalence relations.  In general, a digraph of an equivalence relation falls into connected components that correspond to the parts of the associated partition, with a complete digraph on the points of each part, and no other arcs.  In the present case, the arcs are given as follows:

# Con(''A'') has the structure of a SER on ''S'', with a sling at each of the points in ''S'', two-way arcs between the points of {"''A''",&nbsp;"''i''"}, and two-way arcs between the points of {"''B''",&nbsp;"''u''"}.

# Con(''A'') has the structure of a SER on ''S'', with a sling at each of the points in ''S'', two-way arcs between the points of {"''A''",&nbsp;"''i''"}, and two-way arcs between the points of {"''B''",&nbsp;"''u''"}.