Abstract
We introduce Boolean proximity algebras as a generalization of Efremovič 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.
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Co-operation was supported by EC COST Action 274 “Theory and Applications of Relational Structures as Knowledge Instruments” (TARSKI), www.tarski.org, and NATO Collaborative Linkage Grant PST.CLG 977641.
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Düntsch, I., Vakarelov, D. Region–based theory of discrete spaces: A proximity approach. Ann Math Artif Intell 49, 5–14 (2007). https://doi.org/10.1007/s10472-007-9064-3
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DOI: https://doi.org/10.1007/s10472-007-9064-3