Transformations of Logical Graphs • 4

Semiotic Transformations

Once we bring the dual interpretations of logical graphs to the same Table and relate their parleys to the same objects, it is clear we are dealing with a triadic sign relation of the sort taken up in C.S. Peirce’s semiotics or theory of signs.

A sign relation as a set embedded in a cartesian product tells how the signs in and the interpretant signs in correlate with the objects or objective situations in

There are many ways of using sign relations to model various types of sign‑theoretic situations and processes.  The following cases are often seen.

• Some sign relations model co‑referring signs or transitions between signs within a single language or symbol system.  In that event has
• Other sign relations model translations between different languages or different interpretations of the same language, in other words, different ways of referring the same set of signs to a shared object domain.

The next Table extracts the sign relation involved in switching between existential and entitative interpretations of logical graphs.

• Column 1 shows the object domain as the set of 16 boolean functions on 2 variables.
• Column 2 shows the sign domain as a representative set of logical graphs denoting the objects in according to the existential interpretation.
• Column 3 shows the interpretant domain as the same set of logical graphs denoting the objects in according to the entitative interpretation.

Resources

• C.S. Peirce • On the Definition of Logic
• C.S. Peirce • Logic as Formal Semiotic
• Semeiotic • Sign Relations • Triadic Relations
• Survey of Semiotics, Semiosis, Sign Relations

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