A semantic analysis of some distributive logics with negation
Celani, Sergio Arturo; A semantic analysis of some distributive logics with negation; Jagiellonian University; Reports on Mathematical Logic; 48; 10-2013; 79-98
Celani, Sergio Arturo
In this paper we shall study some extensions of the semilattice based deductive systems S (N) and S (N, 1), where N is the variety of bounded distributive lattices with a negation operator. We shall prove that S (N) and S (N, 1) are the deductive systems generated by the local consequence relation and the global consequence relation associated with ¬-frames, respectively. Using algebraic and relational methods we will prove that S (N) and some of its extensions are canonical and frame complete.