Logics of space with connectedness predicates: complete axiomatizations

In this paper we present a complete quantifier-free axiomatization of several logics on region-based theory of space based on contact relation and connectedness predicates. We prove completeness theorems for the logics in question with respect to three different semantics: algebraic – with respect to several important classes of contact algebras, topological – based on the contact algebras over various classes of topological spaces, and relational semantics with respect to Kripke frames with reflexive and symmetric relations.