[CG] Re: Sign Relations

Sign Relations • Semiotic Equivalence Relations 1 • https://inquiryintoinquiry.com/2024/02/15/sign-relations-semiotic-equivalen… All, A “semiotic equivalence relation” (SER) is a special type of equivalence relation arising in the analysis of sign relations. Generally speaking, any equivalence relation induces a partition of the underlying set of elements, known as the “domain” or “space” of the relation, into a family of equivalence classes. In the case of a SER the equivalence classes are called “semiotic equivalence classes” (SECs) and the partition is called a “semiotic partition” (SEP). The sign relations L_A and L_B have many interesting properties over and above those possessed by sign relations in general. Some of those properties have to do with the relation between signs and their interpretant signs, as reflected in the projections of L_A and L_B on the SI‑plane, notated as proj_{SI} L_A and proj_{SI} L_B, respectively. The dyadic relations on S×I induced by those projections are also referred to as the “connotative components” of the corresponding sign relations, notated as Con(L_A) and Con(L_B), respectively. Tables 6a and 6b show the corresponding connotative components. Tables 6a and 6b. Connotative Components Con(L_A) and Con(L_B) • https://inquiryintoinquiry.files.wordpress.com/2020/06/connotative-componen… A nice property of the sign relations L_A and L_B is that their connotative components Con(L_A) and Con(L_B) form a pair of equivalence relations on their common syntactic domain S = I. This type of equivalence relation is called a “semiotic equivalence relation” (SER) because it equates signs having the same meaning to some interpreter. Each of the semiotic equivalence relations, Con(L_A), Con(L_B) ⊆ S×I ≅ S×S partitions the collection of signs into semiotic equivalence classes. This constitutes a strong form of representation in that the structure of the interpreters’ common object domain {A, B} is reflected or reconstructed, part for part, in the structure of each one's semiotic partition of the syntactic domain {“A”, “B”, “i”, “u”}. It's important to observe the semiotic partitions for interpreters A and B are not identical, indeed, they are “orthogonal” to each other. Thus we may regard the “form” of the partitions as corresponding to an objective structure or invariant reality, but not the literal sets of signs themselves, independent of the individual interpreter's point of view. Information about the contrasting patterns of semiotic equivalence corresponding to the interpreters A and B is summarized in Tables 7a and 7b. The form of the Tables serves to explain what is meant by saying the SEPs for A and B are “orthogonal” to each other. Tables 7a and 7b. Semiotic Partitions for Interpreters A and B • https://inquiryintoinquiry.files.wordpress.com/2020/06/semiotic-partitions-… Resources — Sign Relations • https://oeis.org/wiki/Sign_relation Semiotic Equivalence Relations 1 • https://oeis.org/wiki/Sign_relation#Semiotic_Equivalence_Relations_1 Document History • https://oeis.org/wiki/Sign_relation#Document_history Regards, Jon cc: https://www.academia.edu/community/L6PpAM cc: https://mathstodon.xyz/@Inquiry/111891382765624469