Trace models of concurrent valuation algebras

This paper introduces Concurrent Valuation Algebras (CVAs), a novel extension of ordered valuation algebras (OVAs). CVAs include two combine operators representing parallel and sequential products, adhering to a weak exchange law. This development offers theoretical and practical benefits for the specification and modelling of concurrent and distributed systems. As a presheaf on a space of domains, CVAs enable localised specifications, supporting modularity, compositionality, and the ability to represent large and complex systems. Furthermore, CVAs align with lattice-based refinement reasoning and are compatible with established methodologies such as Hoare and Rely-Guarantee logics. The flexibility of CVAs is explored through three trace models, illustrating distinct paradigms of concurrent/distributed computing, interrelated by morphisms. The paper also highlights the potential to incorporate a powerful local computation framework from valuation algebras for model checking in concurrent and distributed systems. The foundational results presented have been verified with the proof assistant Isabelle/HOL.