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Modal Algebra of Multirelations (2305.11346v2)
Published 18 May 2023 in cs.LO
Abstract: We formalise the modal operators from the concurrent dynamic logics of Peleg, Nerode and Wijesekera in a multirelational algebraic language based on relation algebra and power allegories, using relational approximation operators on multirelations developed in a companion article. We relate Nerode and Wijesekera's box operator with a relational approximation operator for multirelations and two related operators that approximate multirelations by different kinds of deterministic multirelations. We provide an algebraic soundness proof of Goldblatt's axioms for concurrent dynamic logic as an application.