Using Otter for Temporal Resolution

Abstract

This paper describes how to use Otter, a resolution based theorem prover for classical propositional and first-order logics to implement Fisher’s temporal resolution method. Fisher’s clausal temporal resolution method involves both classical-style ‘step’ resolution within states and ‘temporal’ resolution over states. As the translation to a normal form removes most of the temporal operators, and the resolution within states is very similar to resolution in classical logics, most of the inferences required for the step resolution phase can be performed by Otter after a simple translation into classical propositional logic. However, the application of the temporal resolution rule is more complex, requiring a search for sets of formulae that together imply an invariant property, for resolution with an eventuality formula. We suggest how Otter can be used to fulfil the obligations of a particular algorithm that performs this search. The correctness of the method is discussed and we conclude by outlining how it has helped develop a prototype theorem prover based on Fisher’s method.