By Gérard Ligozat

Content material:
Chapter 1 Allen's Calculus (pages 1–28):
Chapter 2 Polynomial Subclasses of Allen's Algebra (pages 29–61):
Chapter three Generalized periods (pages 63–85):
Chapter four Binary Qualitative Formalisms (pages 87–144):
Chapter five Qualitative Formalisms of Arity more than 2 (pages 145–158):
Chapter 6 Quantitative Formalisms, Hybrids, and Granularity (pages 159–185):
Chapter 7 Fuzzy Reasoning (pages 187–222):
Chapter eight The Geometrical technique and Conceptual areas (pages 223–258):
Chapter nine vulnerable Representations (pages 259–304):
Chapter 10 versions of RCC?8 (pages 305–342):
Chapter eleven A express method of Qualitative Reasoning (pages 343–361):
Chapter 12 Complexity of Constraint Languages (pages 363–390):
Chapter thirteen Spatial Reasoning and Modal common sense (pages 391–412):
Chapter 14 functions and software program instruments (pages 413–421):
Chapter 15 end and clients (pages 423–434):

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Example text

4, the last statement is true, since R is dense and unlimited on the left- and right-hand sides. The same would hold true if R was replaced by Q. 5. e. having the same set of solutions) which is algebraically closed. The definition of the property of algebraic closure suggests a way of doing it. In the literature, the corresponding algorithms are called algorithms for enforcing path consistency (or algebraic closure). As already mentioned, enforcing path consistency is based on repeatedly performing the following operation on 3-tuples of vertices (i, j, k): C(i, j) ← C(i, j) ∩ (C(i, k) ◦ C(k, j)) Since each label contains a maximum of 13 basic relations, it is clear that stability is achieved after a finite number of operations.

The other problems are polynomially reducible to it and hence also NP-complete. Given these results, three types of approach evolve if we consider the practical resolution of these problems. We may consider one of the three types of approaches as follows: – complete algorithms, but with exponential time cost; – polynomial, but incomplete, algorithms; – specific algorithms which are complete only in certain cases. We will describe further in detail each one of these approaches. 4. Constraint propagation The technique of constraint propagation is based on the use of two operations: inversion and composition.

The resulting scenario is a consistent refinement; – let us choose the relation f in C(V 1, V 2), f in C(V 1, V 3), and o in C(V 2, V 4). The resulting scenario is a consistent refinement; – let us choose the relation eq in C(V 1, V 2), p in C(V 1, V 3), and o in C(V 2, V 3). The resulting scenario is a consistent refinement. 10. 4. Fundamental problems Given an arbitrary network, the fundamental problems which we consider are the following: – determining if the network is consistent; – if this is the case: - finding an instantiation which satisfies it, - finding a consistent scenario, - computing the minimal network.

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