Construction of Boolean contact algebras

Authors:
Ivo Düntsch;Michael Winter
Affiliations:
Department of Computer Science, Brock University, St. Catharines, Ontario, Canada, L2S 3A1;Department of Computer Science, Brock University, St. Catharines, Ontario, Canada, L2S 3A1
Venue:
AI Communications - Special issue on: 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.