Temporal Resolution Rule Research Articles

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 efficient 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 justified 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.

Removing irrelevant information in temporal resolution proofs

The generation of too much information prohibits efficient resolution proof search in classical logics. Subsumption is used to discard redundant information and strategies have been developed to guide the proof search avoiding irrelevant information. The extension of the resolution method to temporal logics, further magnifies this problem. Here we develop an algorithm for the removal of irrelevant information during resolution proofs for a particular resolution proof system for propositional linear-time temporal logic. The resolution system operates on formulae in a normal form. Following a phase of classical style resolution, temporal resolution is carried out by detecting sets of formulae that together represent an □-formula to be resolved with a ◊-formula. It is before the application of the temporal resolution rule that the new algorithm is applied to efficiently remove irrelevant information. The completeness of the new algorithm is discussed and its complexity considered. Its practical efficiency is demonstrated by giving timings for a set of examples.