Model-Guided Proof Planning

Proof planning is a form of theorem proving in which the proving procedure is viewed as a planning process. The plan operators in proof planning are called methods. In this paper we propose a strategy for heuristically restricting the set of methods to be applied in proof search. It is based on the idea that the plausibility of a method can be estimated by comparing the model class of proof lines newly generated by the method with that of the assumptions and of the theorem. For instance, in forward reasoning when a method produces a new assumption whose model class is not a superset of the model class of the given premises, the method will lead to a situation which is semantically not justified and will not lead to a valid proof in later stages. A semantic restriction strategy is to reduce the search space by excluding methods whose application results in a semantic mismatch. A semantic selection strategy heuristically chooses the method that is likely to make most progress towards filling the gap between the assumptions and the theorem. Each candidate method is evaluated with respect to the subset and superset relation with the given premises. All models considered are taken from a finite reference subset of the full model class. In this contribution we present the model-guided approach as well as first experiments with it.