Trace models of concurrent valuation algebras

This paper introduces Concurrent Valuation Algebras (CVAs), extending ordered valuation algebras (OVAs) by incorporating two combine operators representing parallel and sequential products that adhere to a weak exchange law. CVAs present significant theoretical and practical advantages for specifying and modelling concurrent and distributed systems. As a presheaf on a space of domains, a CVA facilitates localised specifications, promoting modularity, compositionality, and the capability to represent large and complex systems. Moreover, CVAs facilitate lattice-based refinement reasoning, and are compatible with standard methodologies such as Hoare and Rely-Guarantee logics. We demonstrate the flexibility of CVAs through three trace models that represent distinct paradigms of concurrent/distributed computing, and interrelate them via morphisms. We also discuss the potential for importing a powerful local computation framework from valuation algebras for the model checking of concurrent and distributed systems.