06070cam a2200697Mi 4500 ocn828298714 OCoLC 20171107093659.0 m o d cr cnu---unuuu 130223s2013 enkae ob 000 0 eng d 9781118601372 (electronic bk.) 1118601378 (electronic bk.) 9781118601457 (electronic bk.) 1118601459 (electronic bk.) 9781848212527 AU@ 000050718536 CHBIS 009914541 CHVBK 175204519 DEBSZ 431339368 DKDLA 820120-katalog:000696488 NZ1 15916492 DEBBG BV043395462 (OCoLC)828298714 EBLCP eng pn EBLCP N$T YDXCP DG1 UMR E7B IDEBK OCLCF OCLCQ OCLCO DEBSZ OCLCQ COO OCLCQ DEBBG MAIN Q339.25 .L54 2012 MAT 016000 bisacsh MAT 018000 bisacsh 511.3 Ligozat, Gérard. Qualitative Spatial and Temporal Reasoning / [electronic resource] London, UK : ISTE ; Hoboken, N.J. : Wiley, 2012. 1 online resource (xxxi, 505 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references. 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. 1.4.5. Enforcing algebraic closure 1.5. 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. 2.2.8. ORD-Horn relations 2.3. Maximal tractable subclasses of Allen's algebra; 2.3.1. An alternative characterization of pre-convex relations; 2.3.2. The other maximal polynomial subclasses; 2.4. Using polynomial subclasses; 2.4.1. Ladkin and Reinefeld's algorithm; 2.4.2. Empirical study of the consistency problem; 2.5. Models of Allen's language; 2.5.1. Representations of Allen's algebra; 2.5.2. Representations of the time-point algebra; 2.5.3. [aleph-null] categoricity of Allen's algebra; 2.6. Historical note; Chapter 3. Generalized Intervals; 3.1. "When they built the bridge." 3.1.1. Towards generalized intervals 3.2. 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. 3.9. Conclusions 3.10. 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; 4.7. The Rectangle calculus. 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. Print version record. Qualitative reasoning. Spatial analysis (Statistics) Space and time Mathematical models. Logic, Symbolic and mathematical. Space and time Mathematical models. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Logic, Symbolic and mathematical. fast (OCoLC)fst01002068 Qualitative reasoning. fast (OCoLC)fst01084939 Space and time Mathematical models. fast (OCoLC)fst01127627 Spatial analysis (Statistics) fast (OCoLC)fst01128784 Electronic books. Print version: Ligozat, Gérard. Qualitative spatial and temporal reasoning. London, UK : ISTE ; Hoboken, N.J. : Wiley, 2012 9781848212527 (DLC) 2011029658 (OCoLC)699765430 http://onlinelibrary.wiley.com/book/10.1002/9781118601457 Wiley Online Library ddc BK 206470 206470