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A Relation-Algebraic Approach to Multirelations and Predicate Transformers

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Mathematics of Program Construction (MPC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9129))

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Abstract

The correspondence between up-closed multirelations and isotone predicate transformers is well known. Less known is that multirelations have also been used for modelling topological contact, not only computations. We investigate how properties from these two lines of research translate to predicate transformers. To this end, we express the correspondence of multirelations and predicate transformers using relation algebras. It turns out to be similar to the correspondence between contact relations and closure operations. Many results generalise from up-closed to arbitrary multirelations.

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Acknowledgments

We thank Hitoshi Furusawa and Georg Struth for pointing out related work and the anonymous referees for making helpful comments.

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Authors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Kiel, Germany

    Rudolf Berghammer

  2. Department of Computer Science and Software Engineering, University of Canterbury, Christchurch, New Zealand

    Walter Guttmann

Authors
  1. Rudolf Berghammer
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  2. Walter Guttmann
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Correspondence to Walter Guttmann .

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Editors and Affiliations

  1. University of Oxford, Oxford, UK

    Ralf Hinze

  2. University of Bonn, Bonn, Germany

    Janis Voigtländer

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Berghammer, R., Guttmann, W. (2015). A Relation-Algebraic Approach to Multirelations and Predicate Transformers. In: Hinze, R., Voigtländer, J. (eds) Mathematics of Program Construction. MPC 2015. Lecture Notes in Computer Science(), vol 9129. Springer, Cham. https://doi.org/10.1007/978-3-319-19797-5_3

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  • DOI: https://doi.org/10.1007/978-3-319-19797-5_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19796-8

  • Online ISBN: 978-3-319-19797-5

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