Self-Extensionality of Finitely-Valued Logics: Advances

EasyChair Preprint 6563, version 12

Abstract

We start from proving a general characterization of the self-extensionality of sentential logics implying the decidability of this problem for (not necessarily uniform) finitely-valued logics. And what is more, in case of logics defined by finitely many either implicative or both disjunctive and conjunctive hereditarily simple finite hereditarily simple (viz., having no non-simple submatrix) matrices, we then derive a characterization yielding a quite effective algebraic criterion of checking their self-extensionality via analyzing homomorphisms between (viz., in the uniform case, endomorphisms of) the underlying algebras of their defining matrices and equally being a quite useful heuristic tool, manual applications of which are demonstrated within the framework of Łukasiewicz' finitely-valued logics, logics of three-valued super-classical matrices, four-valued expansions of Belnap's "useful" four-valued logic as well as their (not necessarily uniform) no-more-than-three-valued extensions, [uniform inferentially consistent non-]classical [three-valued] ones proving to be [non-]self-extensional.

Keyphrases: logic, matrix, model

@booklet{EasyChair:6563,
  author    = {Alexej Pynko},
  title     = {Self-Extensionality of Finitely-Valued Logics: Advances},
  howpublished = {EasyChair Preprint 6563},
  year      = {EasyChair, 2022}}