LEADER 05503nam 2200709 a 450 001 9910814774803321 005 20240313144330.0 010 $a1-118-60156-4 010 $a1-118-60145-9 010 $a1-118-60137-8 035 $a(CKB)2670000000336698 035 $a(EBL)1124705 035 $a(OCoLC)828298714 035 $a(SSID)ssj0000833974 035 $a(PQKBManifestationID)11461911 035 $a(PQKBTitleCode)TC0000833974 035 $a(PQKBWorkID)10955118 035 $a(PQKB)10261242 035 $a(MiAaPQ)EBC1124705 035 $a(Au-PeEL)EBL1124705 035 $a(CaPaEBR)ebr10660573 035 $a(CaONFJC)MIL527833 035 $a(EXLCZ)992670000000336698 100 $a20110819d2012 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aQualitative spatial and temporal reasoning /$fGe?rard Ligozat 205 $a1st ed. 210 $aLondon, U.K. $cISTE ;$aHoboken, N.J. $cWiley$d2012 215 $a1 online resource (539 p.) 225 1 $aISTE 300 $aDescription based upon print version of record. 311 $a1-84821-252-6 320 $aIncludes bibliographical references (p. [471]-500) and index. 327 $aCover; 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 327 $a1.4.5. 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 327 $a2.2.8. 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 an 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. ?0-categoricity of Allen's algebra; 2.6. Historical note; Chapter 3.neralized Intervals; 3.1. ""When they built the bridge" 327 $a3.1.1. 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 327 $a3.9. 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 327 $a4.7. The Rectangle calculus 330 $aStarting with an updated description of Allen's calculus, the book proceeds with a description of the main qualitative calculi which have been developed over the last two decades. It describes the connection of complexity issues to geometric properties. Models of the formalisms are described using the algebraic notion of weak representations of the associated algebras. The book also includes a presentation of fuzzy extensions of qualitative calculi, and a description of the study of complexity in terms of clones of operations. 410 0$aISTE 606 $aQualitative reasoning 606 $aSpatial analysis (Statistics) 606 $aSpace and time$xMathematical models 606 $aLogic, Symbolic and mathematical 615 0$aQualitative reasoning. 615 0$aSpatial analysis (Statistics) 615 0$aSpace and time$xMathematical models. 615 0$aLogic, Symbolic and mathematical. 676 $a511.3 700 $aLigozat$b Ge?rard$01597188 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910814774803321 996 $aQualitative spatial and temporal reasoning$93918841 997 $aUNINA