Taming Multirelations
Hitoshi Furusawa, Georg Struth
TL;DR
This paper explores the algebraic structure of multirelations, extending binary relations with set associations, and develops axiom systems for their operations and iterations in various algebraic contexts.
Contribution
It introduces a comprehensive algebraic framework for multirelations, including axioms for union, intersection, composition, and iteration, bridging set-theoretic and algebraic perspectives.
Findings
Axioms for multirelations in bi-monoids and bi-quantales
Characterization of multirelation operations and iteration
Foundations for algebraic reasoning about multirelations
Abstract
Binary multirelations generalise binary relations by associating elements of a set to its subsets. We study the structure and algebra of multirelations under the operations of union, intersection, sequential and parallel composition, as well as finite and infinite iteration. Starting from a set-theoretic investigation, we propose axiom systems for multirelations in contexts ranging from bi-monoids to bi-quantales.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Logic, programming, and type systems · Formal Methods in Verification