Proof systems for satisfiability in Hennessy-Milner Logic with recursion

Abstract

An extension of Hennessy-Milner Logic with recursion is presented. A recursively specified formula will have two standard interpretations: a minimal one and a maximal one. Minimal interpretations of formulas are useful for expressing liveness properties of processes, whereas maximal interpretations are useful for expressing safety properties. We present sound and complete proof systems for both interpretations for when a process satisfies a (possibly recursive) formula. The rules of the proof systems consist of an introduction rule for each possible structure of a formula and are intended to extend the work of Stirling and Winskel. Moreover the proof systems may be presented directly in PROLOG to yield a decision procedure for verifying when a finite-state process satisfies a specification given as a (possibly recursive) formula.