A tableau proof system for a mazurkiewicz trace logic with fixpoints

Abstract

We present a tableau based proof system for νTrTL, a trace based temporal logic with fixpoints. The proof system generalises similar systems for standard interleaving temporal logics with fixpoints. In our case special attention has to be given to the modal rule: First we give a system with an interleaving style modal rule, later we use a technique similar to the sleep set method (known from finite state model checking) to obtain a more efficient proof rule. We briefly highlight the relation of the improved rule with recent advances in tableau systems for classical propositional logic, the tamed cut of the system KE.

The treatment of fixpoints leads to possibly infinite tableaux, which however can be finitely represented, yielding treelike structures with back loops: we show this using an automata construction. Indirectly we obtain a (known) decidability result.