A semantic analysis of some distributive logics with negation

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.Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires.facultad de Ciencias Exactas; Argentin