qualitative constraint network
Condotta
In this paper, we focus on a recently introduced problem in the context of spatial and temporal qualitative reasoning, called the MAX-QCN problem. This problem involves obtaining a spatial or temporal configuration that maximizes the number of satisfied constraints in a qualitative constraint network (QCN). To efficiently solve the MAX-QCN problem, we introduce and study two families of encodings of the partial maximum satisfiability problem (PMAX-SAT). Each ofthese encodings is based on, what we call, a forbidden covering with regard to the composition table of the considered qualitative calculus. Intuitively, a forbidden covering allows us to express, in a more or less compact manner, the non-feasible configurations for three spatial or temporal entities.The experimentation that we have conducted with qualitative constraint networks from the Interval Algebra shows the interest of our approach.
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Exact Learning of Qualitative Constraint Networks from Membership Queries
Mouhoub, Malek, Marri, Hamad Al, Alanazi, Eisa
A Qualitative Constraint Network (QCN) is a constraint graph for representing problems under qualitative temporal and spatial relations, among others. More formally, a QCN includes a set of entities, and a list of qualitative constraints defining the possible scenarios between these entities. These latter constraints are expressed as disjunctions of binary relations capturing the (incomplete) knowledge between the involved entities. QCNs are very effective in representing a wide variety of real-world applications, including scheduling and planning, configuration and Geographic Information Systems (GIS). It is however challenging to elicit, from the user, the QCN representing a given problem. To overcome this difficulty in practice, we propose a new algorithm for learning, through membership queries, a QCN from a non expert. In this paper, membership queries are asked in order to elicit temporal or spatial relationships between pairs of temporal or spatial entities. In order to improve the time performance of our learning algorithm in practice, constraint propagation, through transitive closure, as well as ordering heuristics, are enforced. The goal here is to reduce the number of membership queries needed to reach the target QCN. In order to assess the practical effect of constraint propagation and ordering heuristics, we conducted several experiments on randomly generated temporal and spatial constraint network instances. The results of the experiments are very encouraging and promising.
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A Class of df-Consistencies for Qualitative Constraint Networks
Condotta, Jean-François (CRIL) | Lecoutre, Christophe (CRIL)
In this paper, we introduce a new class of local consistencies, called df-consistencies, for qualitative constraint networks. Each consistency of this class is based on weak composition and a mapping f that provides a covering for each relation of the considered qualitative calculus. We study the connections existing between some properties of the introduced mappings and the relative inference strength of df-consistencies. The consistency obtained by the usual closure under weak composition corresponds to the weakest element of the class, whereas df-consistencies stronger than weak composition open new promising perspectives. Interestingly, the class of df-consistencies is shown to form a complete lattice where the partial order denotes the relative strength of every two consistencies. We also propose a generic algorithm that allows us to compute the closure of qualitative constraint networks under any "well-behaved" consistency of the class. The experimentation that we have conducted on qualitative constraint networks from the Interval Algebra shows the interest of these new local consistencies, in particular for the consistency problem.
Qualitative CSP, Finite CSP, and SAT: Comparing Methods for Qualitative Constraint-based Reasoning
Westphal, Matthias (University of Freiburg) | Wölfl, Stefan (University of Freiburg)
Qualitative Spatial and Temporal Reasoning (QSR) is concerned with constraint-based formalisms for representing, and reasoning with, spatial and temporal information over infinite domains. Within the QSR community it has been a widely accepted assumption that genuine qualitative reasoning methods outperform other reasoning methods that are applicable to encodings of qualitative CSP instances. Recently this assumption has been tackled by several authors, who proposed to encode qualitative CSP instances as finite CSP or SAT instances. In this paper we report on the results of a broad empirical study in which we compared the performance of several reasoners on instances from different qualitative formalisms. Our results show that for small-sized qualitative calculi (e.g., Allen's interval algebra and RCC-8) a state-of-the-art implementation of QSR methods currently gives the most efficient performance. However, on recently suggested large-size calculi, e.g., OPRA4, finite CSP encodings provide a considerable performance gain. These results confirm a conjecture by Bessière stating that support-based constraint propagation algorithms provide better performance for large-sized qualitative calculi.
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