Construction of Boolean contact algebras

Authors:
Ivo Düntsch;Michael Winter
Affiliations:
Department of Computer Science, Brock University, St. Catharines, Ontario, Canada, L2S 3A1 E-mail: {duentsch,mwinter}@cosc.brocku.ca;Department of Computer Science, Brock University, St. Catharines, Ontario, Canada, L2S 3A1 E-mail: {duentsch,mwinter}@cosc.brocku.ca
Venue:
AI Communications - Spatial and Temporal Reasoning
Year:
2004

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Abstract

We consider Boolean algebras endowed with a contact relation which are abstractions of Boolean algebras of regular closed sets together with Whitehead's connection relation [17], in which two non-empty regular closed sets are connected if they have a non-empty intersection. These are standard examples for structures used in qualitative reasoning, mereotopology, and proximity theory. We exhibit various methods how such algebras can be constructed and give several non-standard examples, the most striking one being a countable model of the Region Connection Calculus in which every proper region has infinitely many holes.Both authors gratefully acknowledge support by the National Sciences and Engineering Research Council of Canada.