Semantic Characterizations for Reachability and Trace Equivalence in a Linear Logic-Based Process Calculus (Preliminary Report)

We give semantic characterizations for the notions of reachability and trace equivalence in a linear-logic based framework of asyncronous concurrent process calculus. Usually the reachability relation in linear logic-based concurrent process calculi is characterized by the logical notion of provability, which is in turn characterized by model-theoretic semantics such as the phase semantics. The standard phase semantics is, however, too abstract to give concrete meanings to processes due to the presence of the closure operation. To remedy this, we introduce a simplification of the phase semantics, which we call the naive phase semantics, and show that the reachability relation is also characterized by the completeness with respect to the naive phase semantics. On the other hand, the logical provability does not provide any satisfactory notion of equivalence over processes. We consider the trace equivalence (Hoare[Hoa80]) for our process calculus and introduce certain algebraic models, which we call the trace semantics. Then the trace equivalence is characterized by the completeness with respect to the trace semantics.