Résolution de contraintes du premier ordre dans la théorie des arbres finis ou infinis

Thi-Bich-Hanh Dao (1)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166

We present in this paper an algorithm, in the theory $\Tt\,$ 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 $\Ff$. The algorithm consists of a set of 11 rewrite rules. It transforms a first order formula in a conjunction of ``solved'' formulae, equivalent in $\Tt$, which has not new free variables and which is such that, (1) the conjunction either is the constant logic $\true$ or is reduced to $\neg\true$, or has at least one free variable and is equivalent neither to $\true$ nor to $\false$, (2) each solved formula can be transformed immediately in a Boolean combination of basic formulae whose length does not exceed twice the length of the solved formula. The basic formulae are particular cases of existentially quantified conjunctions of equations. The correctness of the algorithm gives another proof of the completeness of $\Tt$ demonstrated by Michael Maher. We end with benchmarks realized by an implementation, solving formulae with more than 160 nested alternated quantifiers.

Domaines: Intelligence artificielle [cs.AI]

Thi-Bich-Hanh Dao. Résolution de contraintes du premier ordre dans la théorie des arbres finis ou infinis. JFPLC, 2000, Marseille, France. pp.225-240. ⟨hal-00144920⟩