A clausal resolution method for CTL branching-time temporal logic

In this paper we extend our clausal resolution method for linear time temporal logics to a branching-time framework. Thus, we propose an e cient deductive method useful in a variety of applications requiring an expressive branching-time temporal logic in AI. The branching-time temporal logic considered is Computation Tree Logic (CTL), often regarded as the simplest useful logic of this class. The key elements of the resolution method, namely the normal form, the concept of step resolution and a novel temporal resolution rule, are introduced and justi ed with respect to this logic. A completeness argument is provided, together with some examples of the use of the temporal resolution method. Finally, we consider future work, in particular the extension of the method yet further, to Extended CTL (ECTL), which is CTL extended with fairness operators, and CTL , the most powerful logic of this class. We will also outline possible implementation of the approach by adapting techniques developed for linear-time temporal resolution.