An algebraic approach to multirelations and their properties

We study operations and equational properties of multirelations, which have been used for modelling games, protocols, computations, contact, closure and topology. The operations and properties are expressed using sets, heterogeneous relation algebras and more general algebras for multirelations. We investigate the algebraic properties of a new composition operation based on the correspondence to predicate transformers, different ways to express reflexive-transitive closures of multirelations, numerous equational properties, how these properties are connected and their preservation by multirelational operations. We particularly aim to generalise results and properties from up-closed multirelations to arbitrary multirelations. This paper is an extended version of [7].