Region---based theory of discrete spaces: A proximity approach

Authors:
Ivo Düntsch;Dimiter Vakarelov
Affiliations:
Department of Computer Science, Brock University, St Catharines, Canada L2S 3A1;Department of Mathematical Logic, Sofia University, Sofia, Bulgaria
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2007

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Abstract

We introduce Boolean proximity algebras as a generalization of Efremovi驴 proximities which are suitable in reasoning about discrete regions. Following Stone's representation theorem for Boolean algebras, it is shown that each such algebra is isomorphic to a substructure of a complete and atomic Boolean proximity algebra.