Folding Transformation Rules for Constraint Logic Programs

We consider the folding transformation rule for constraint logic programs. We propose an algorithm for applying the folding rule in the case where the constraints are linear equations and inequations over the rational or the real numbers. Basically, our algorithm consists in reducing a rule application to the solution of one or more systems of linear equations and inequations. We also introduce two variants of the folding transformation rule. The first variant combines the folding rule with the clause splitting rule, and the second variant eliminates the existential variables of a clause, that is, those variables which occur in the body of the clause and not in its head. Finally, we present the algorithms for applying these variants of the folding rule

Building and Combining Matching Algorithms

International audienceThe concept of matching is ubiquitous in declarative programming and in automated reasoning. For instance, it is a key mechanism to run rule-based programs and to simplify clauses generated by theorem provers. A matching problem can be seen as a particular conjunction of equations where each equation has a ground side. We give an overview of techniques that can be applied to build and combine matching algorithms. First, we survey mutation-based techniques as a way to build a generic matching algorithm for a large class of equational theories. Second, combination techniques are introduced to get combined matching algorithms for disjoint unions of theories. Then we show how these combination algorithms can be extended to handle non-disjoint unions of theories sharing only constructors. These extensions are possible if an appropriate notion of normal form is computable

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

Matching in a Class of Combined Non-Disjoint Theories

Colloque avec actes et comité de lecture. internationale.International audienceSolving equational problems is an ubiquitous process in automated deduction, where one needs for instance unification in completion procedures to compute critical pairs, and matching to apply rewrite rules. We present new equational matching and unification results in some combinations of non-disjoint equational theories. Some results are already known for theories sharing an appropriate notion of constructors. We investigate the idea of considering theories that are not explicitly based on the notion of constructors. In this direction, a new class of theories is presented, where a theory is defined as a union of two subtheories, one such that shared symbols do not affect the behavior of the theory, and another one given by a term rewrite system on shared symbols. Matching and unification problems are studied for this class of theories, and for unions of theories in this class. Results obtained for the matching problem are particularly relevant