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International Conference on Relational and Algebraic Methods in Computer Science

RAMICS 2012: Relational and Algebraic Methods in Computer Science pp 207–218Cite as

Relational Representation Theorem for Powerset Quantales

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7560))

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.

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Author information

Authors and Affiliations

  1. Department of Information Systems, Faculty of Environmental and Information Studies, Tottori University of Environmental Studies, Japan

    Koki Nishizawa

  2. Department of Mathematics and Computer Science, Kagoshima University, Japan

    Hitoshi Furusawa

Authors
  1. Koki Nishizawa
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  2. Hitoshi Furusawa
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Editor information

Editors and Affiliations

  1. Department of Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Wolfram Kahl

  2. Computer Laboratory, University of Cambridge, 15 JJ Thomson Avenue, CB3 0FD, Cambridge, UK

    Timothy G. Griffin

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© 2012 Springer-Verlag Berlin Heidelberg

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Nishizawa, K., Furusawa, H. (2012). Relational Representation Theorem for Powerset Quantales. In: Kahl, W., Griffin, T.G. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2012. Lecture Notes in Computer Science, vol 7560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33314-9_14

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  • DOI: https://doi.org/10.1007/978-3-642-33314-9_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33313-2

  • Online ISBN: 978-3-642-33314-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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