Contact Algebras and Region-based Theory of Space: A Proximity Approach – I

Article type: Research Article

Authors: Dimov, Georgi | Vakarelov, Dimiter

Affiliations: Department of Mathematics and Computer Science, University of Sofia, Blvd. James Bourchier 5, 1126 Sofia, Bulgaria. E-mail: {gdimov,dvak}@fmi.uni-sofia.bg

Abstract: This work is in the field of region-based (or Whitehedian) theory of space, which is an important subfield of Qualitative Spatial Reasoning (QSR). The paper can be considered also as an application of abstract algebra and topology to some problems arising and motivated in Theoretical Computer Science and QSR. Different axiomatizations for region-based (or Whiteheadian) theory of space are given. The most general one is introduced under the name "Contact Algebra" Adding some extra first- or secondorder axioms to those of contact algebras, some new or already known algebraic notions are obtained. Representation theorems and completion theorems for all such algebras are proved. Extension theories of the classes of all semiregular T_0-spaces and all N-regular (a notion introduced here) T_1-spaces are developed.

Keywords: Qualitative Spatial Reasoning, mereological relations, contact relations, contact algebras, region-based theories of space, RCC models, representation theorems, extensions, completion

Journal: Fundamenta Informaticae, vol. 74, no. 2-3, pp. 209-249, 2006