Self-Extensionality of Finitely-Valued Logics

EasyChair Preprint 4928, version 3

Abstract

We start from proving a general characterization of the self-extensionality of sentential logics implying the decidability of this problem as for (possibly, multiple) finitely-valued logics. And what is more, in case of finitely-valued logics with equality determinant as well as either implication or both conjunction and disjunction, we then derive a characterization yielding a quite effective algebraic criterion of checking their self-extensionality via analyzing homomorphisms between (viz., in the unitary case, endomorphisms of) their underlying algebras and equally being a quite useful heuristic tool, manual applications of which are demonstrated within the framework of Łukasiewicz' finitely-valued logics, four-valued expansions of Belnap's "useful" four-valued logic, their non-unitary three-valued extensions, unitary inferentially consistent non-classical ones being well-known to be non-self-extensional, as well as unitary three-valued disjunctive (in particular, implicative) logics with subclassical negation (including both paraconsistent and paracomplete ones).

Keyphrases: logic, matrix, model

@booklet{EasyChair:4928,
  author    = {Alexej Pynko},
  title     = {Self-Extensionality of Finitely-Valued Logics},
  howpublished = {EasyChair Preprint 4928},
  year      = {EasyChair, 2021}}