Hennessy-Milner Completeness in Transition Systems with Synchronous Concurrent Composition

We consider the problem of obtaining Hennessy-Milner soundness and completeness-the coincidence of logical equivalence and bisimilarity-in the setting of transition systems with synchronous concurrent composition. Starting from a richly expressive modal logic, motivated by resource semantics and distributed systems modelling, including both additive and multiplicative propositional connectives and also additive and multiplicative action modalities, as well as certain first-order quantifiers, we establish sufficient conditions for Hennessy-Milner soundness and completeness to hold. We develop two examples in detail. First, using the propositional part of the logic, we consider a calculus of resources and processes, explaining how the semantics may be refined to give a familiar equational theory. Second, employing a first-order, arithmetic theory, we consider a calculus with utilities that is able to express optimality and equilibria in resource allocation. Abstract. We consider the problem of obtaining Hennessy-Milner sound-ness and completeness — the coincidence of logical equivalence and bisimilarity — in the setting of transition systems with synchronous concurrent composition. Starting from a richly expressive modal logic, motivated by resource semantics and distributed systems modelling, including both additive and multiplicative propositional connectives and also additive and multiplicative action modalities, as well as certain first-order quantifiers, we establish sucient conditions for Hennessy–Milner soundness and completeness to hold. We develop two examples in detail. First, using the propositional part of the logic, we consider a calculus of resources and processes, explaining how the semantics may be refined to give a familiar equational theory. Second, employing a first-order, arithmetic theory, we consider a calculus with utilities that is able to express optimality and equilibria in resource allocation.