Relational representation theorem for powerset quantales

Authors:
Koki Nishizawa;Hitoshi Furusawa
Affiliations:
Department of Information Systems, Faculty of Environmental and Information Studies, Tottori University of Environmental Studies, Japan;Department of Mathematics and Computer Science, Kagoshima University, Japan
Venue:
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
Year:
2012

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The weakest prespecification

Information Processing Letters
Topology via logic

Topology via logic

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Abstract

The paper gives a sufficient condition for a quantale to be isomorphic to a sub-quantale of the quantale whose elements are binary relations on a set and whose order and monoid structure are respectively given by inclusion and relational composition and the identity relation. A quantale has such a relational representation, if its underlying lattice is a powerset of some set. We also show some other equivalent conditions of the sufficient condition.