[CG] Re: Sign Relations

Sign Relations • Dyadic Aspects • https://inquiryintoinquiry.com/2024/02/11/sign-relations-dyadic-aspects-b/ All, For an arbitrary triadic relation L ⊆ O×S×I, whether it happens to be a sign relation or not, there are 6 dyadic relations obtained by projecting L on one of the planes of the OSI‑space O×S×I. The 6 dyadic projections of a triadic relation L are defined and notated as shown in Table 2. Table 2. Dyadic Aspects of Triadic Relations • https://inquiryintoinquiry.files.wordpress.com/2020/06/dyadic-projections-o… By way of unpacking the set‑theoretic notation, here is what the first definition says in ordinary language. • The dyadic relation resulting from the projection of L on the OS‑plane O×S is written briefly as L_OS or written more fully as proj_{OS}(L) and is defined as the set of all ordered pairs (o, s) in the cartesian product O×S for which there exists an ordered triple (o, s, i) in L for some element i in the set I. In the case where L is a sign relation, which it becomes by satisfying one of the definitions of a sign relation, some of the dyadic aspects of L can be recognized as formalizing aspects of sign meaning which have received their share of attention from students of signs over the centuries, and thus they can be associated with traditional concepts and terminology. Naturally, traditions vary as to the precise formation and usage of such concepts and terms. Other aspects of meaning have not received their fair share of attention and thus remain innominate in current anatomies of sign relations. Resources — Sign Relations • https://oeis.org/wiki/Sign_relation Dyadic Aspects • https://oeis.org/wiki/Sign_relation#Dyadic_Aspects Document History • https://oeis.org/wiki/Sign_relation#Document_history Regards, Jon cc: https://www.academia.edu/community/lPxxxP cc: https://mathstodon.xyz/@Inquiry/111891382765624469