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We present in this paper an algorithm, in the theory T of (eventually infinite) trees, for solving constraints represented by full first order formulae, with equality as the only relation and with symbols of function taken in an infinite set F. The algorithm consists of a set of 11 rewrite rules. It transforms a first order formula in a conjunction of "… (More)

Prolog, which stands for PROgramming in LOGic, is the most widely used language in the logic programming paradigm. One of its main concepts is unification. It represents the mechanism of binding the contents of variables and can be seen as solving conjunctions of equations over finite or infinite trees. We present in this paper an idea of a first-order… (More)

In recent years, clustering has been extended to constrained clustering, so as to integrate knowledge on objects or on clusters, but adding such constraints generally requires to develop new algorithms. We propose a declarative and generic framework, based on Constraint Programming, which enables to design clustering tasks by specifying an optimization… (More)

Although the observation of grammaticality judgements is well acknowledged, their formal representation faces problems of different kinds: linguistic, psycholinguistic, logical, computational. In this paper we focus on addressing some of the logical and computational aspects, relegating the linguistic and psycholinguistic ones in the parameter space. We… (More)

In this paper, we present an abstract framework for learning a finite domain constraint solver mod-eled by a set of operators enforcing a consistency. The behavior of the consistency to be learned is taken as the set of examples on which the learning process is applied. The best possible expression of this operator in a given language is then searched. We… (More)

We present in this paper an algorithm in the theory <i>T</i> of possibly infinite trees for solving general constraints represented by full first-order formulas, with equality as the only relation and functional symbols taken from an infinite set <b>F</b>. The algorithm consists of a set of 11 rewriting rules. It transforms a first-order formula <i>p</i> in… (More)

We present in this paper an automatic way to combine any first-order theory T with the theory of finite or infinite trees. First of all, we present a new class of theories that we call zero-infinite-decomposable and show that every decomposable theory T accepts a decision procedure in the form of six rewriting rules which for every first order proposition… (More)