The external version of a subclassical logic

TL;DR

This paper investigates the semantic properties of the external version of three-valued subclassical logics, expanding the language with unary connectives and analyzing their model-theoretic characteristics.

Contribution

It provides necessary and sufficient conditions for models of L to be models of its external version L^e, and explores distinctive semantic features of L^e.

Findings

Characterization of models of L^e based on models of L

Identification of semantic properties unique to L^e

Extension of the language with external operators and their implications

Abstract

A three-valued logic L is subclassical when it is defined by a single matrix having the classical two-element matrix as a subreduct. In this case, the language of L can be expanded with special unary connectives, called external operators. The resulting logic L^e is the external version of L, a notion originally introduced by D. Bochvar in 1938 with respect to his weak Kleene logic. In this paper we study the semantic properties of the external version of a three-valued subclassical logic L. We determine sufficient and necessary conditions to turn a model of L into a model of L^e . Moreover, we establish some distinctive semantic properties of L^e.