Kleisli, Parikh and Peleg compositions and liftings for multirelations

https://doi.org/10.1016/j.jlamp.2017.04.002Get rights and content
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Highlights

  • Relational formalisations of Kleisli, Parikh and Peleg compositions and liftings of multirelations are provided.

  • Some of properties of these compositions are clarified in relation-algebraic style.

  • Subclasses of multirelations that form categories with each composition are given.

Abstract

Multirelations provide a semantic domain for computing systems that involve two dual kinds of nondeterminism. This paper presents relational formalisations of Kleisli, Parikh and Peleg compositions and liftings of multirelations. These liftings are similar to those that arise in the Kleisli category of the powerset monad. We show that Kleisli composition of multirelations is associative, but need not have units. Parikh composition may neither be associative nor have units, but yields a category on the subclass of up-closed multirelations. Finally, Peleg composition has units, but need not be associative; a category is obtained when multirelations are union-closed.

Keywords

Algebras of multirelations
Liftings of multirelations
Associativity of compositions of multirelations
Relational calculus

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