A Resolution Method For CTL Branching-Time Temporal Logic

In this paper we extend our clausal resolution method for linear temporal logics to a branching-time framework. The branching-time temporal logics considered are Computation Tree Logic (CTL), often regarded as the simplest useful logic of this class, and Extended CTL (ECTL), which is CTL extended with fairness operators. 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 justified with respect to both these logics. A completeness argument is provided, together with an example of the use of the temporal resolution method. Finally, we consider future work, in particular extension of the method yet further, to CTL , and implementation of the approach by utilising techniques developed for linear-time temporal resolution.