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Monotone Predicate Transformers as Up-Closed Multirelations

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Relations and Kleene Algebra in Computer Science (RelMiCS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4136))

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Abstract

In the study of semantic models for computations two independent views predominate: relational models and predicate transformer semantics. Recently the traditional relational view of computations as binary relations between states has been generalised to multirelations between states and properties allowing the simultaneous treatment of angelic and demonic nondeterminism. In this paper the two-level nature of multirelations is exploited to provide a factorisation of up-closed multirelations which clarifies exactly how multirelations model nondeterminism. Moreover, monotone predicate transformers are, in the precise sense of duality, up-closed multirelations. As such they are shown to provide a notion of effectivity of a specification for achieving a given postcondition.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Stellenbosch, South Africa

    Ingrid Rewitzky & Chris Brink

Authors
  1. Ingrid Rewitzky
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  2. Chris Brink
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Editors and Affiliations

  1. School of Computer Science, The University of Manchester,  

    Renate A. Schmidt

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© 2006 Springer-Verlag Berlin Heidelberg

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Rewitzky, I., Brink, C. (2006). Monotone Predicate Transformers as Up-Closed Multirelations. In: Schmidt, R.A. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2006. Lecture Notes in Computer Science, vol 4136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11828563_21

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  • DOI: https://doi.org/10.1007/11828563_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37873-0

  • Online ISBN: 978-3-540-37874-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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