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 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

Interval-based data refinement: A uniform approach to true concurrency in discrete and real-time systems

“…From a true concurrency perspective, action refinement in a causal process-algebraic setting is studied in [36,37] and a modal logic for reasoning about true concurrency is given in [5]. Formal approaches to real-time systems refinement has a long history (e.g., [26,47,28,35,41,40]), but these frameworks must often use additional constraints to cope with timing-related delays.…”

The Glory of the Past and Geometrical Concurrency

“…The absorbtion law example is used in [1,19] to show that hhbisimulation has strictly more distinguishing power than h-bisimulation; where in [7] Figure 6: Conflicting futures of [1]. Example 3.10 (non-binary conflict and the need for event identifiers) This example is taken from [7, ex.4.8] where it is meant to illustrate that the event identifier logic indeed needs the event variables in order to make the distinction between the two concurrent systems which are distinguishable by the hh-bisimulation (the other examples of that paper can be distinguished by the logic without the need of event variables).…”

“…The natural question now is what small extension of this logic can capture the finest, hereditary history preserving bisimulation. This question becomes more interesting in the light of the fact that two recent logic developments [1,7] study concurrency bisimulations (including hh) over concurrency models strictly less expressive than HDAs, yet using event-identifier variables inside more complex modalities.…”

“…The other feature of hHDML is that it is a modal logic defined over HDA, which are a model of true concurrency that is more expressive than the other models on which the logics of [1,7] are defined (i.e., is more expressive than event structures or configuration structures). Therefore this makes it a good framework for investigating and comparing all these logics in a uniform manner; similar to what is done in [18] on comparing expressiveness of concurrency models by embedding them into HDA (i.e., defining the exact class of HDA that they capture); or similar to [5] where translations are made between logics that all capture the same bisimulation.…”

“…Therefore this makes it a good framework for investigating and comparing all these logics in a uniform manner; similar to what is done in [18] on comparing expressiveness of concurrency models by embedding them into HDA (i.e., defining the exact class of HDA that they capture); or similar to [5] where translations are made between logics that all capture the same bisimulation. Moreover, the simple syntax and natural interpretation of hHDML in the style of standard modal logic makes it a good candidate for investigating modal characterizations of the spectrum of true concurrency bisimulations [8,19,21], as was done with modal logics for standard process equivalences in [17] and recently using event identifier modalities in [1].…”