[CG] Re: Transformations of Logical Graphs

Transformations of Logical Graphs • 4 • https://inquiryintoinquiry.com/2024/05/08/transformations-of-logical-graphs… 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” L ⊆ O × S × I, as a set L embedded in a cartesian product O × S × I, tells how the “signs” in S and the “interpretant signs” in I correlate with the “objects” or objective situations in O. 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 L ⊆ O × S × I has S = I. • 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 L ⊆ O × S × I involved in switching between existential and entitative interpretations of logical graphs. Interpretive Duality as Sign Relation • https://inquiryintoinquiry.files.wordpress.com/2021/03/peirce-duality-as-si… • Column 1 shows the object domain O as the set of 16 boolean functions on 2 variables. • Column 2 shows the sign domain S as a representative set of logical graphs denoting the objects in O according to the existential interpretation. • Column 3 shows the interpretant domain I as the same set of logical graphs denoting the objects in O according to the entitative interpretation. Resources — C.S. Peirce • On the Definition of Logic • https://inquiryintoinquiry.com/2012/06/01/c-s-peirce-on-the-definition-of-l… C.S. Peirce • Logic as Formal Semiotic • https://inquiryintoinquiry.com/2012/06/04/c-s-peirce-logic-as-semiotic/ Semeiotic • Sign Relations • Triadic Relations • https://oeis.org/wiki/Semeiotic • https://oeis.org/wiki/Sign_relation • https://oeis.org/wiki/Triadic_relation Survey of Semiotics, Semiosis, Sign Relations • https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign… Regards, Jon cc: https://www.academia.edu/community/laaO6E