Logics for extended distributive contact lattices. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Ivanova, T.
• Is Part Of: Journal of applied non-classical logics. Volume 28:Issue 1(2018)
• Page Start: 140
• Page End: 162
• Publication Date: 2018-01-02
• Subjects: Mereotopology -- distributive mereotopology -- contact algebras -- extended distributive contact lattices -- spacial logics -- completeness theorems; Nonclassical mathematical logic -- Periodicals; Wiskundige logica; Logic; Periodicals; 511.3105
• DOI: 10.1080/11663081.2017.1373562
• Languages: English
• ISSNs: 1166-3081

Abstract

Abstract: 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 true in all contact algebras. The structures in, 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.