Modal Logic and Equality for Process Algebra

This paper provides a denotational semantics for the ‘saturation method’, described by J. A. Bergstra and J. W. Klop, in the form of a modal logic. In particular the semantics describes congruence for CCS processes in the form of a modal logic whose axioms are a modal representation of the tau laws. The main idea of the paper is to represent bisimulation equivalences of CCS in terms of a simple modal logic K. This logic is a variant of the classical modal logic K introducing a plus operator to mirror the choice operator of CCS. Weak bisimulation equivalence and process equality can be characterized in terms of extra axioms added to K. In the case of equality the axioms are a modal representation of the tau laws. A CCS process maps to a model of the logic; two processes are equivalent if they map to the same model