  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.
