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Informationen zum Autor Gérard Ligozat held the position of Researcher in Mathematics and Computer Science at the CNRS, and was a Professor of Computer Science at the University of Paris-Sud, France. He was offered a professorship in computer science at Adam Mickiewicz University, Poznan, Poland, where he taught Artificial Intelligence in 2008. He has been working on the subject of qualitative temporal and spatial reasoning for the past 25 years. Klappentext 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. Zusammenfassung * 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. Inhaltsverzeichnis Introduction. Qualitative Reasoning xvii Chapter 1. Allen's Calculus 1 1.1. Introduction 1 1.2. Allen's interval relations 6 1.3. Constraint networks 8 1.4. Constraint propagation 17 1.5. Consistency tests 26 Chapter 2. Polynomial Subclasses of Allen's Algebra 29 2.1. "Show me a tractable relation!" 29 2.2. Subclasses of Allen's algebra 30 2.3. Maximal tractable subclasses of Allen's algebra 52 2.4. Using polynomial subclasses 57 2.5. Models of Allen's language 60 2.6. Historical note 61 Chapter 3. Generalized Intervals 63 3.1. "When they built the bridge . " 63 3.2. Entities and relations 65 3.3. The lattice of basic (p, q)-relations 68 3.4. Regions associated with basic (p, q)-relations 69 3.5. Inversion and composition 73 3.6. Subclasses of relations: convex and pre-convex relations 79 3.7. Constraint networks 82 3.8. Tractability of strongly pre-convex relations 83 3.9. Conclusions 84 3.10. Historical note 85 Chapter 4. Binary Qualitative Formalisms 87 4.1. "Night driving" 87 4.2. Directed points in dimension 1 92 4.3. Directed intervals 97 4.4. The OPRA direction calculi 99 4.5. Dipole calculi 100 4.6. The Cardinal direction calculus 101 4.7. The Rectangle calculus 104 4.8. The n-point calculus 106 4.9. The n-block calculus 108 4.10. Cardinal directions between regions 109 4.11. The INDU calculus 123 4.12. The 2n-star calculi 126 4.13. The Cyclic interval calculus 128 4.14. The RCC-8 formalism 131 4.15. A discrete RCC theory 137 Chapter 5. Qualitative Formalisms of Arity Greater than 2 145 5.1. "The sushi bar" 145 5.2. Ternary spatial and temporal formalisms 146 5.3. Alignment relations between regions 155 5.4. Conclusions 158 Chapter 6. Quantitative Formalisms, Hybrids, and Granularity 159 6.1. "Did John meet Fred this morning?"159 6.2. TCSP metric networks 160 6.3. Hybrid networks 164 6.4. Meiri's formalism 168 6.5. Disjunctive linear relations (DLR) 174 6.6. Generalized temporal networks 175 6.7. Networks with granularity 179 Chapter 7. Fuzzy Reasoning 187 7.1. "Picasso's Blue period" 187 7.2. Fuzzy relations between classical intervals 188 7.3. Events and fuzzy intervals 195 7.4. Fuzzy spatial reasoning: a fuzzy RCC 208 7.5. Historical note 2...
