THE EXTERNAL VERSION OF A SUBCLASSICAL LOGIC

Abstract A three-valued logic 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 can be expanded with special unary connectives, called external operators . The resulting logic is called the external version of , 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 . We determine sufficient and necessary conditions to turn a model of into a model of . Moreover, we establish some distinctive semantic properties of .