Logics for extended distributive contact lattices

摘要

The notion of contact algebra is one of the main tools in the region-based theory of space. It is an extension of Boolean algebra with an additional relation C called contact. There are some problems related to the motivation of the operation of Boolean complementation. Because of this operation is dropped and the language of distributive lattices is extended by considering as non-definable primitives the relations of contact, nontangential inclusion and dual contact. It is obtained an axiomatization of the theory consisting of the universal formulas in the language L(0,1; +, •; ≤,C,Ĉ, «) true in all contact algebras. The structures in L, satisfying the axioms in question, are called extended distributive contact lattices (EDC-lattices). In this paper we consider several logics, corresponding to EDCL We give completeness theorems with respect to both algebraic and topological semantics for these logics. It turns out that they are decidable.