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Brock TR # CS-04-01 Abstract

Construction of Boolean contact algebras    [PDF]
Ivo Düntsch and Michael Winter, January 2004.

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, 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.