A Logic for True Concurrency

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 are also recovered as a fragment. We believe that this contributes to a rational presentation of the true concurrent spectrum and to a deeper understanding of the relations between the involved behavioural equivalences.