This article is a revised and extended version of our earlier work which appeared in Proceedings of the 3rd International Symposium on Requirements Engineering (1997), pages 78 -- 86; Authors' addresses: A. Hunter, Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK; email: A.Hunter@cs.ucl.ac.uk; B. Nuseibeh, Department of Computing, Imperial College, 180 Queen's Gate, London, SW7 2BZ, UK; email: ban@doc.ic.ac.uk.

. 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. 1 Introduction Few years ago, we have developed a --- refutationally complete --- method combining search for refutations (proofs) and models (counter-examples) for first order formulae...

. A significant extension of a model building method is presented. A quite complete, albeit reasonably short, description of the former method is given in order to make this paper self-contained. The extension allows to handle Presburger arithmetic and to deduce inductive consequences from sets of Horn clauses. For a large class of programs it also permit to deduce negative facts and to detect non termination. It is shown how the extended method can be used in verifying and correcting programs. Logic programs verification and correction is emphasized, but the same techniques work for imperative programs as evidenced by an example. Models are built incrementally --- feature particularly important in software reusing. The proposed method verifies programs w.r.t. formal specifications, but its fundamentals (i.e. model building) allows to point out errors and suggests the way of correcting wrong programs also w.r.t. informal specifications, such as specifications by examples: : : (this is ...

. Minimal Herbrand models of sets of first-order clauses are useful in several areas of computer science, e.g. automated theorem proving, program verification, logic programming, databases, and artificial intelligence. In most cases, the conventional model generation algorithms are inappropriate because they generate nonminimal Herbrand models and can be inefficient. This article describes an approach for generating the minimal Herbrand models of sets of first-order clauses. The approach builds upon positive unit hyperresolution (PUHR) tableaux, that are in general smaller than conventional tableaux. PUHR tableaux formalize the approach initially introduced with the theorem prover SATCHMO. Two minimal model generation procedures are described. The first one expands PUHR tableaux depth-first relying on a complement splitting expansion rule and on a form of backtracking involving constraints. A Prolog implementation, named MM-SATCHMO, of this procedure is given and its performance on ben...

. A powerful extension of the tableau method is described. It consists in a new simplification rule allowing to prune the search space and a new way of extracting a model from a given (possibly infinite) branch. These features are combined with a former method for simultaneous search for refutations and models. The possibilities of the new method w.r.t. the original one are clearly stated. In particular it is shown that the method is able to build model for each formula having a model expressible by equational constraints. 1. Introduction The construction and the use of models or counter-examples are crucial techniques widely used in all aspects of human reasoning. In mathematics, models allow the rejection of false conjectures or help to prove theorems. Incorporating such abilities into automated theorem provers is therefore a very natural idea, which has been considered since the beginning [15, 25]. Nevertheless, it is not until the nineties that feasible methods have been proposed ...