Self-Extensionality of Finitely-Valued Logics: Advances

EasyChair Preprint 6563, version 4

Abstract

We start from proving a general characterization
of the self-ex\-ten\-si\-o\-na\-li\-ty 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 {\em 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 \L{}ukasiewicz'
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, 2021}}