# Nouvelles techniques pour la construction de modèles finis ou infinis en déduction automatique

Abstract : In this thesis, we present several new techniques for model building in Automated Deduction. In the first part, we propose a general method for building finite models that favourably compares with the most powerful existing finite model builders. In the second part, we investigate methods for simultaneous search for refutations and (infinite, Herbrand) models. We improve the methods RAMC (Refutation And Model Construction) and RAMCET (Refutation And Model Construction with Equational Tableaux) defined by R. Caferra and N. Zabel by defining new rules and strategies. These extensions strictly increase the capabilities of the methods both for model building and unsatisfiability detection. We show that some of the proposed methods are uniform decision procedures for a wide range of decidable classes. We show the limits of the formalism of equational constraints, previously used for representing Herbrand models, and we propose to extend it by including terms with integer exponents ($I$-terms) and tree automata. As a new result, we prove the decidability of the first-order theory of $I$-terms. Fourthly, we study some applications of our work: we present a new approach for discovering and using analogy in simultaneous search for refutations and models, and we show how to use the method RAMC in Logic Programming (for extending logic program interpreters, detecting and correcting errors in logic programs etc.). Finally we describe the system RAMC-ATINF implementing our approach and we report some experiments showing the practical capabilities of our method.
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Theses

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### Identifiers

• HAL Id : tel-00004960, version 1

### Citation

Nicolas Peltier. Nouvelles techniques pour la construction de modèles finis ou infinis en déduction automatique. Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 1997. Français. ⟨tel-00004960⟩

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