Splitting atoms in relational algebras

Authors:
Prathap Siddavaatam;Michael Winter
Affiliations:
Department of Computer Science, Brock University, St. Catharines, Ontario, Canada;Department of Computer Science, Brock University, St. Catharines, Ontario, Canada
Venue:
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Year:
2011

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Abstract

Splitting atoms in a relation algebra is a common tool to generate new algebras from old ones. This includes constructing nonrepresentable algebras from representable structures. The known method of splitting atoms does not allow that bijections different from the identity are contained in the starting algebra. This is a major drawback of that method because interesting candidates in mereotopology do contain such bijections. An ad-hoc splitting was done in those examples, and the results have been published in several papers. With this paper we want to start a thorough investigation of possible splitting methods.