Relaxation of Qualitative Constraint Networks Dominique D’Almeida, Jean-François Condotta, Christophe Lecoutre, and Lakhdar Saïs CRIL-CNRS, Université d’Artois, rue de l’Université, 62307 Lens, France {dalmeida,condotta,lecoutre,sais}@cril.univ-artois.fr Abstract. In this paper, we propose to study the interest of relaxing qualitative constraints networks by using the formalism of discrete Con- straint Satisfaction Problem (CSP). This allows us to avoid the intro- duction of new definitions and properties in the domain of qualitative reasoning. We first propose a general (but incomplete) approach to show the unsatisfiability of qualitative networks, by using a relaxation on any set of relations. Interestingly enough, for some qualitative calculi, the proposed scheme can be extended to determine the satisfiability of any qualitative network, leading to an original, simple and complete method. However, as the efficiency of our approach depends on the chosen relax- ation, total relations should be preferred due to their connections with the hardness of constraint networks. We then present some preliminary experimental results, with respect to unsatisfiability, which show some promising improvements on some classes of random qualitative networks. 1 Introduction The need for reasoning about time and space arises in many areas of Artificial Intelligence, including computer vision, natural language understanding, geo- graphic information systems (GIS), scheduling, planning, diagnosis and genetics. Numerous formalisms for representing and reasoning about time and space in a qualitative way have been proposed in the past two decades [1,28,22,3,27,19,4]. Those formalisms involve a finite set of basic relations denoting qualitative relationships between temporal or spatial entities. Intersection, overlapping, con- tainment, precedence are examples of such qualitative relationships. For instance, in the field of qualitative reasoning about temporal data, there is a well-known formalism called Allen’s calculus [1]. It is based on intervals of the rational line for representing temporal entities and thirteen basic relations between such in- tervals are used to represent the qualitative situations between temporal entities: an interval can follow another one, meet another one, and so on. Typically, Qualitative Constraint Networks (QCNs) are used to express infor- mation on a spatial or temporal situation. Each constraint of a QCN represents a set of acceptable qualitative configurations between some temporal or spatial entities and is defined by a set of basic relations. The total relation, which is the set of all basic relations, is the term used to describe a total uncertainty in the configurations. The density of such relations in a qualitative networks can take part to the difficulty to solve those problems. I. Miguel and W. Ruml (Eds.): SARA 2007, LNAI 4612, pp. 93–108, 2007. c  Springer-Verlag Berlin Heidelberg 2007