A Framework for Merging Qualitative Constraints Networks

Spatial or temporal reasoning is an important task for many applications in Artificial Intelligence, such as space scheduling, navigation of robots, etc. Several qualitative approaches have been proposed to represent spatial and temporal entities and their relations. These approaches consider the qualitative aspects of the space relations only, disregarding any quantitative measurement. In some applications, e. g. multi-agent systems, spatial or temporal information concerning a set of objects may be conflicting. This paper highlights the problem of merging spatial or temporal qualitative constraints networks. We propose a merging operator which, starting from a set of possibly conflicting qualitative constraints networks, returns a consistent set of spatial or temporal information representing the result of merging. Introduction Representing and reasoning about time and space is an important task in many domains such as natural language processing, geographic information systems, computer vision, robot navigation. Many qualitative approaches have been proposed to represent the spatial or temporal entities and their relations. The majority of these formalisms however use qualitative constraints networks (QCNs) to represent information about a system. In some application, e. g. multi-agent systems, spatial or temporal information come from different sources, i. e. each source provides a spatial or temporalQCN representing relative positions between objects. The multiplicity of sources providing spatial or temporal information makes that the underlying QCNs are generally conflicting. Indeed it becomes necessary to solve the conflicts and define a set of consistent spatial or temporal information representing the result of merging. This is the focus of the present paper. Merging multiple sources information has attracted much attention in the framework of (weighted) propositional logic (Revesz 1997; Konieczny & Pérez 1998; Cholvy 1998; Benferhat et al. 1999; 2002; Konieczny, Lang, & Marquis 2004). In this paper, we take our inspiration from these works (in particular those proposed in the framework of Copyright c © 2008, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. propositional logic) and propose a procedure for merging QCNs. The rest of this paper is organized as follows. We first present a necessary background on qualitative formalisms for representing space or time, in particular qualitative constraints networks. Then we present the problem of dealing with multiple sources providing spatial or temporal information. Before we propose a procedure for merging QCNs. Lastly we conclude. Qualitative formalisms for space and time It is natural to use a particular spatial or temporal qualitative algebra to describe non-numerical relationships between spatial or temporal entities (Allen 1981; van Beek 1990; Vilain, Kautz, & Van Beek 1990; Nebel & Bürckert 1995; Egenhofer 1991; Randell, Cui, & Cohn 1992; Mitra 2004). A qualitative algebra uses a limited range of relations between spatial or temporal objects. These relations can be topological relations (Randell, Cui, & Cohn 1992) (thus the objects represent areas of points), or based on an ordering relation. When representing temporal information, we often use precedence relations between ponctual entities or interval entities (Allen 1981; Vilain, Kautz, & Van Beek 1990). Figure 1 illustrates the basic relations of a well known qualitative formalism, the cardinal directions algebra (Ligozat 1998). It represents the set Bcard composed of the nine basic relations of the cardinal directions algebra, used to represent relative positions of points of the plan provided with an orthogonal reference mark. Given an initial point P = (x1, y1) (with x1 the projection of P according to axis x, and y1 its projection according to axis y), the plan is split into nine areas, each corresponding to a basic relation of Bcard. For example, the relation se (for south east) corresponds to the area of points Q = (x2, y2) such that x2 > x1 and y2 < y1. Formally, a qualitative algebra considers a finite set B of binary relations defined on a domain D. Each of these relations is called a basic relation and represents a particular qualitative situation between two elements of D. These relations are complete and mutually exclusive, namely two elements of D satisfy one and only one basic relation of B. X B Y with B ∈ B, X , Y ∈ D stands for ”(X,Y ) satisfies the basic relation B”. A particular relation of B is the identity relation (eq). Each relation B of B is associated to an Proceedings of the Twenty-First International FLAIRS Conference (2008)