Structural Completeness of Three-Valued Logics with Subclassical Negation

EasyChair Preprint 5171

Abstract

A propositional logic|calculus is said to be structurally complete,
whenever it cannot be extended by non-derivable rules
without deriving new axioms.
Here, we study this property within the framework of
three-valued logics with subclassical negation (3VLSN)
precisely specified and comprehensively marked semantically here.
The principal contribution of the paper is then an effective ---
in case of finitely many connectives --- algebraic criterion
of the structural completeness of any paraconsistent/``both
disjunctive and paracomplete'' 3VLSN, according to which
it is structurally complete ``only if''/iff it is
maximally paraconsistent/paracomplete, that is,
has no proper paraconsistent/paracomplete extension,
and ``only if''/if it has no classical extension.
On the other hand, any [not necessarily] classical logic with[out] theorems
is [not] structurally complete.
In this connection, we also obtain equally effective
algebraic criteria of the mentioned properties
within the general framework of 3VLSN.

Keyphrases: Calculus, extension, logic, matrix

@booklet{EasyChair:5171,
  author    = {Alexej Pynko},
  title     = {Structural Completeness of Three-Valued Logics with Subclassical Negation},
  howpublished = {EasyChair Preprint 5171},
  year      = {EasyChair, 2021}}