A Logic for True Concurrency

Abstract

We propose a logic for true concurrency whose formulae predicate about events in computations and their causal dependencies. The induced logical equivalence is hereditary history-preserving bisimilarity, and fragments of the logic can be identified which correspond to other true concurrent behavioural equivalences in the literature: step, pomset and history-preserving bisimilarity. Standard Hennessy-Milner logic, and thus (interleaving) bisimilarity, is also recovered as a fragment. We also propose an extension of the logic with fixpoint operators, thus allowing to describe causal and concurrency properties of infinite computations. This work contributes to a rational presentation of the true concurrent spectrum and to a deeper understanding of the relations between the involved behavioural equivalences.