Monotone Predicate Transformers as Up-Closed Multirelations

  • Ingrid Rewitzky
  • Chris Brink
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4136)


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.


Binary Relation Boolean Algebra Monotone Operator Semantic Model Bijective Correspondence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ingrid Rewitzky
    • 1
  • Chris Brink
    • 1
  1. 1.Department of Mathematical SciencesUniversity of StellenboschSouth Africa

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