Qualitative Spatial and Temporal Reasoning

✍ Scribed by Ligozat, Gérard

• Publisher: Wiley
• Year: 2013
• Tongue: English
• Leaves: 539
• Series: ISTE
• Category: Library

✦ Synopsis

Cover; Qualitative Spatial and Temporal Reasoning; Title Page; Copyright Page; Table of Contents; Introduction. Qualitative Reasoning; Chapter 1. Allen's Calculus; 1.1. Introduction; 1.1.1. ""The mystery of the dark room""; 1.1.2. Contributions of Allen's formalism; 1.2. Allen's interval relations; 1.2.1. Basic relations; 1.2.2. Disjunctive relations; 1.3. Constraint networks; 1.3.1. Definition; 1.3.2. Expressiveness; 1.3.3. Consistency; 1.4. Constraint propagation; 1.4.1. Operations: inversion and composition; 1.4.2. Composition table; 1.4.3. Allen's algebra; 1.4.4. Algebraic closure.;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 of Contents

3.9. Conclusions3.10. Historical note
Chapter 4. Binary Qualitative Formalisms
4.1. ""Night driving""
4.1.1. Parameters
4.1.2. A panorama of the presented formalisms
4.2. Directed points in dimension 1
4.2.1. Operations
4.2.2. Constraint networks
4.2.3. Networks reducible to point networks
4.2.4. Arbitrary directed point networks
4.3. Directed intervals
4.3.1. Operations
4.3.2. Constraint networks and complexity
4.4. The OPRA direction calculi
4.5. Dipole calculi
4.6. The Cardinal direction calculus
4.6.1. Convex and pre-convex relations
4.6.2. Complexity. 3.1.1. Towards generalized intervals3.2. Entities and relations
3.3. The lattice of basic (p, q)-relations
3.4. Regions associated with basic (p, q)-relations
3.4.1. Associated polytopes
3.4.2. M-convexity of the basic relations
3.5. Inversion and composition
3.5.1. Inversion
3.5.2. Composition
3.5.3. The algebras of generalized intervals
3.6. Subclasses of relations: convex and pre-convex relations
3.6.1. (p, q)-relations
3.6.2. Convex relations
3.6.3. Pre-convex relations
3.7. Constraint networks
3.8. Tractability of strongly pre-convex relations
3.8.1. ORD-Horn relations. 1.4.5. Enforcing algebraic closure1.5. Consistency tests
1.5.1. The case of atomic networks
1.5.2. Arbitrary networks
1.5.3. Determining polynomial subsets
Chapter 2. Polynomial Subclasses of Allen's Algebra
2.1. ""Show me a tractable relation!""
2.2. Subclasses of Allen's algebra
2.2.1. A geometrical representation of Allen's relations
2.2.2. Interpretation in terms of granularity
2.2.3. Convex and pre-convex relations
2.2.4. The lattice of Allen's basic relations
2.2.5. Tractability of convex relations
2.2.6. Pre-convex relations
2.2.7. Polynomiality of pre-convex relations. Cover
Qualitative Spatial and Temporal Reasoning
Title Page
Copyright Page
Table of Contents
Introduction. Qualitative Reasoning
Chapter 1. Allen's Calculus
1.1. Introduction
1.1.1. ""The mystery of the dark room""
1.1.2. Contributions of Allen's formalism
1.2. Allen's interval relations
1.2.1. Basic relations
1.2.2. Disjunctive relations
1.3. Constraint networks
1.3.1. Definition
1.3.2. Expressiveness
1.3.3. Consistency
1.4. Constraint propagation
1.4.1. Operations: inversion and composition
1.4.2. Composition table
1.4.3. Allen's algebra
1.4.4. Algebraic closure.

✦ Subjects

Logic, Symbolic and mathematical;MATHEMATICS--Infinity;MATHEMATICS--Logic;Qualitative reasoning;Space and time--Mathematical models;Spatial analysis (Statistics);Electronic books;Space and time -- Mathematical models;MATHEMATICS -- Infinity;MATHEMATICS -- Logic