The external version of a subclassical logic

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.