Model building and interactive theory discovery

Abstract

We show how our former approach to model building can be extended into a unified approach to model building and model checking, able to guide the discovery of theories in which a model can be built for a given formula. In contrast with other enumeration approaches used to decide some classes of first-order formulae, our approach automatically discovers (in the best case) or strongly guides (in the worst case) discovery of such theories. For practical reasons, the method has been developed in resolution style and implemented as an extension of a resolution-based theorem prover, but the same principles can be applied to the connexion method, tableaux ⋯ and of course the models built by our method can be used by theorem provers based on other calculi. Detailed examples are given for the new notions.