Dynamic Mereotopology: A Point-free Theory of Changing Regions. I. Stable and unstable mereotopological relations

Issue title: Understanding Computers' Intelligence Celebrating the 100th Volume of Fundamenta Informaticae in Honour of Helena Rasiowa

Article type: Research Article

Authors: Vakarelov, Dimiter

Affiliations: Sofia University, Faculty of Mathematics and Computer Science blvd James Bouchier 5, 1126 Sofia, Bulgaria. E-mail: dvak@fmi.univ-sofia.bg

Abstract: In this paper we present a point-free theory of Whiteheadean style of space and time. Its algebraic formulation, called dynamic contact algebra (DCA), is a Boolean algebra whose elements symbolized dynamic regions changing in time, with two spatio-temporal mereotopological relations between them: stable and unstable contact. We prove several representation theorems for DCAs, representing them in structures arising from products of contact algebras or from products of topological spaces. We also present a decidable quantifier-free constraint logic for reasoning about stable and unstable mereotopological relations between dynamic regions. We consider the paper as a first step in point-free dynamic mereotopology.

Keywords: Dynamicmereotopology, point-free theory of space and time, topological representation theorem, spatio-temporal logic

DOI: 10.3233/FI-2010-268

Journal: Fundamenta Informaticae, vol. 100, no. 1-4, pp. 159-180, 2010