Di-Algebraic Semantics of Logics

Abstract

In [22] the problem of the logics corresponding to topological quasi-boolean algebras [27, 1] has been recently solved by the present author. The semantics provided involved convex amalgams of boolean algebras with additional total and partial operations. Canonical extensions of the structure was also investigated. In the present research, this semantics is generalized to a wide class of logics including distributive logics. It is also shown that the semantics is a proper generalization of the general theory of algebraizable logics due to Blok-Pigozzi [5] and Czelakowski [7].