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The dyadic components of sign relations can be given graph-theoretic representations, as ''digraphs'' (or ''directed graphs''), that provide concise pictures of their structural and potential dynamic properties.

The dyadic components of sign relations can be given graph-theoretic representations, as ''digraphs'' (or ''directed graphs''), that provide concise pictures of their structural and potential dynamic properties.

By way of terminology, a directed edge ‹''x'', ''y''› is called an ''arc'' from point ''x'' to point ''y'', and a self-loop ‹''x'', ''x''› is called a ''sling'' at ''x''.

By way of terminology, a directed edge <math>(x, y)</math> is called an ''arc'' from point <math>x</math> to point <math>y</math>, and a self-loop <math>(x, x)</math> is called a ''sling'' at <math>x</math>.

The denotative components Den(''A'') and Den(''B'') can be represented as digraphs on the six points of their common world set ''W'' = ''O''&nbsp;&cup;&nbsp;''S''&nbsp;&cup;&nbsp;''I'' = {''A'',&nbsp;''B'',&nbsp;"''A''",&nbsp;"''B''",&nbsp;"''i''",&nbsp;"''u''"}.  The arcs are given as follows:

The denotative components <math>\operatorname{Den}(\text{A})</math> and <math>\operatorname{Den}(\text{B})</math> can be represented as digraphs on the six points of their common world set <math>W = O \cup S \cup I = \{ \text{A}, \text{B}, {}^{\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>.  The arcs are given as follows:

# Den(''A'') has an arc from each point of {"''A''",&nbsp;"''i''"} to ''A'' and from each point of {"''B''",&nbsp;"''u''"} to ''B''.

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

# Den(''B'') has an arc from each point of {"''A''",&nbsp;"''u''"} to ''A'' and from each point of {"''B''",&nbsp;"''i''"} to ''B''.

 

:: <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.

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.