A Modal µ-Calculus and a Proof System for Value Passing Processes

Abstract

A first-order modal ¯-calculus is introduced as a convenient logic for reasoning about processes with value passing. For this logic we present a proof system for model checking sequential processes defined in the value passing CCS. Soundness of the proof system is established. The use of the system is demonstrated on two small but instructive examples. 1 Introduction The propositional modal ¯-calculus is a particularly expressive logic for reasoning about branching-time properties of communicating systems. Many other logics, like dynamic logic and CTL, have uniform encodings in this logic [11]. Over the last decade, many proof systems for checking validity of formulae of this logic w.r.t. particular states (or sets of states) of particular models have been proposed. Since the semantics of the logic is given w.r.t. labelled transition systems (LTS), some of these proof systems [1,4,6,7,15] refer directly to LTS, while other, compositional approaches [2,8] refer to descriptions in some ..