Starting with an updated description of Allen’s calculus, the book
proceeds with a description of the main qualitative calculi which
have been developed over the last two decades. It describes
the connection of complexity issues to geometric properties. Models
of the formalisms are described using the algebraic notion of weak
representations of the associated algebras. The book also includes
a presentation of fuzzy extensions of qualitative calculi, and a
description of the study of complexity in terms of clones of
operations.
Table des matières
Introduction. Qualitative Reasoning xvii
Chapter 1. Allen’s Calculus 1
Chapter 2. Polynomial Subclasses of Allen’s Algebra 29
Chapter 3. Generalized Intervals 63
Chapter 4. Binary Qualitative Formalisms 87
Chapter 5. Qualitative Formalisms of Arity Greater than 2145
Chapter 6. Quantitative Formalisms, Hybrids, and Granularity159
Chapter 7. Fuzzy Reasoning 187
Chapter 8. The Geometrical Approach and Conceptual Spaces223
Chapter 9. Weak Representations 259
Chapter 10. Models of RCC-8 305
Chapter 11. A Categorical Approach of Qualitative Reasoning343
Chapter 12. Complexity of Constraint Languages 363
Chapter 13. Spatial Reasoning and Modal Logic 391
Chapter 14. Applications and Software Tools 413
Chapter 15. Conclusion and Prospects 423
Appendix A. Elements of Topology 435
Appendix B. Elements of Universal Algebra 451
Appendix C. Disjunctive Linear Relations 463
Bibliography 471
Index 501
A propos de l’auteur
Gérard Ligozat is retired professor of computer science, Paris-Sud University.
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