Abstract

. The use of regular tree grammars to represent and build models of formulae of first-order logic without equality is investigated. The combination of regular tree grammars with equational constraints provides a powerful and general way of representing Herbrand models. We show that the evaluation problem (i.e. the problem of finding the truth value of a formula in a given model) is decidable when models are represented in the way we propose. We also define a method to build such representations of models for first-order formulae. These results are a powerful extension of our former method for simultaneous search for refutations and models. Keywords: Automated Deduction, Model Building, Tree Automata, Regular Tree Grammars. 1. Introduction The problem of building models or counter-examples of first-order formulae is a very important one, particularly in the field of automated deduction. Besides their intrinsic interest for disproving conjectures, counter-examples (models) have numerous...

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