## Abstract

Modal logic and equality for process algebra
**Modal logic and equality for process algebra**
WPR. Mitchell
Department of Computer Science, University of Manchester, Manchester M13 9PL, UK
ABSTRACT

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^{[oplus]}. 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^{[oplus]}. 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.

Pages: 123
- 138

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