Qualitative spatiotemporal representation and reasoning: a computational perspective

Although there has always been a temptation in KR to set the sights either too low (and provide only a data structuring facility with little or no inference) or too high (and provide a full theorem proving facility), this paper argues for the rich world of representation that lies between these two extremes.

[1]  O. Stock.  Spatial and Temporal Reasoning , 1899 .

[2]  M. Stone.  Applications of the theory of Boolean rings to general topology , 1937 .

[3]  A. Tarski.  Der Aussagenkalkül und die Topologie , 1938 .

[4]  Tang Tsao-Chen.  Algebraic postulates and a geometric interpretation for the Lewis calculus of strict implication , 1938 .

[5]  J. C. C. McKinsey,et al.  A Solution of the Decision Problem for the Lewis systems S2 and S4, with an Application to Topology , 1941, J. Symb. Log..

[6]  A. Tarski,et al.  The Algebra of Topology , 1944 .

[7]  A. Grzegorczyk.  Undecidability of Some Topological Theories , 1951 .

[8]  Abraham Robinson,et al.  Elementary properties of ordered abelian groups , 1960 .

[9]  H. Läuchli,et al.  On the elementary theory of linear order , 1966 .

[10]  Michael Dummett,et al.  Modal Logics Between S4 and S5 , 1967 .

[11]  Johan Anthory Willem Kamp,et al.  Tense logic and the theory of linear order , 1968 .

[12]  Albert R. Meyer,et al.  WEAK MONADIC SECOND ORDER THEORY OF SUCCESSOR IS NOT ELEMENTARY-RECURSIVE , 1973 .

[13]  Larry Joseph Stockmeyer,et al.  The complexity of decision problems in automata theory and logic , 1974 .

[14]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[15]  John P. Burgess,et al.  Logic and time , 1979, Journal of Symbolic Logic.

[16]  A. Nakamura,et al.  On the size of refutation Kripke models for some linear modal and tense logics , 1980 .

[17]  Leslie Lamport,et al.  "Sometime" is sometimes "not never": on the temporal logic of programs , 1980, POPL '80.

[18]  Edmund M. Clarke,et al.  Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic , 1981, Logic of Programs.

[19]  Bowman L. Clarke,et al.  A calculus of individuals based on "connection" , 1981, Notre Dame J. Formal Log..

[20]  J.F.A.K. van Benthem,et al.  Modal logic and classical logic , 1983 .

[21]  James F. Allen.  Maintaining knowledge about temporal intervals , 1983, CACM.

[22]  James F. Allen.  Towards a General Theory of Action and Time , 1984, Artif. Intell..

[23]  A. P. Sistla,et al.  The complexity of propositional linear temporal logics , 1985, JACM.

[24]  John P. Burgess,et al.  The decision problem for linear temporal logic , 1985, Notre Dame J. Formal Log..

[25]  Pierre Wolper,et al.  The tableau method for temporal logic: an overview , 1985 .

[26]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[27]  Joseph Y. Halpern,et al.  “Sometimes” and “not never” revisited: on branching versus linear time temporal logic , 1986, JACM.

[28]  Henry A. Kautz,et al.  Constraint propagation algorithms for temporal reasoning: a revised report , 1989 .

[29]  Yde Venema,et al.  Expressiveness and Completeness of an Interval Tense Logic , 1990, Notre Dame J. Formal Log..

[30]  Ellen Hays.  On Defining Motion Verbs and Spatial Prepositions , 1990, Repräsentation und Verarbeitung räumlichen Wissens.

[31]  Johan de Kleer,et al.  Readings in qualitative reasoning about physical systems , 1990 .

[32]  J. R. Büchi.  On a Decision Method in Restricted Second Order Arithmetic , 1990 .

[33]  Ernest Davis,et al.  Representations of commonsense knowledge , 2014, notThenot Morgan Kaufmann series in representation and reasoning.

[34]  Max J. Egenhofer,et al.  Reasoning about Binary Topological Relations , 1991, SSD.

[35]  Yoav Shoham,et al.  A propositional modal logic of time intervals , 1991, JACM.

[36]  MAX J. EGENHOFER,et al.  Point Set Topological Relations , 1991, Int. J. Geogr. Inf. Sci..

[37]  Anthony G. Cohn,et al.  A Spatial Logic based on Regions and Connection , 1992, KR.

[38]  Stephan Merz,et al.  Decidability and incompleteness results for first-order temporal logics of linear time , 1992, J. Appl. Non Class. Logics.

[39]  Terence R. Smith,et al.  Algebraic approach to spatial reasoning , 1992, Int. J. Geogr. Inf. Sci..

[40]  Valentin Goranko,et al.  Using the Universal Modality: Gains and Questions , 1992, J. Log. Comput..

[41]  Zohar Manna,et al.  The Temporal Logic of Reactive and Concurrent Systems , 1991, Springer New York.

[42]  Benjamin Kuipers,et al.  Qualitative spatial reasoning about objects in motion: application to physics problem solving , 1994, Proceedings of the Tenth Conference on Artificial Intelligence for Applications.

[43]  Brandon Bennett,et al.  Spatial Reasoning with Propositional Logics , 1994, KR.

[44]  Dov M. Gabbay,et al.  Temporal logic (vol. 1): mathematical foundations and computational aspects , 1994 .

[45]  Dov M. Gabbay,et al.  Handbook of logic in artificial intelligence and logic programming (Vol. 4): epistemic and temporal reasoning , 1995 .

[46]  Laure Vieu,et al.  Toward a Geometry of Common Sense: A Semantics and a Complete Axiomatization of Mereotopology , 1995, IJCAI.

[47]  Patrick J. Hayes,et al.  The second naive physics manifesto , 1995 .

[48]  Bernhard Nebel,et al.  Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra , 1994, JACM.

[49]  Dimitris Papadias,et al.  Topological Inference , 1995, IJCAI.

[50]  Mark Stefik,et al.  Introduction to knowledge systems , 1995 .

[51]  Zohar Manna,et al.  Temporal verification of reactive systems - safety , 1995 .

[52]  Brandon Bennett,et al.  Modal Logics for Qualitative Spatial Reasoning , 1996, Log. J. IGPL.

[53]  Alberto Zanardo,et al.  Branching-time logic with quantification over branches: The point of view of modal logic , 1996, Journal of Symbolic Logic.

[54]  Michael F. Worboys,et al.  The Algebraic Structure of Sets of Regions , 1997, COSIT.

[55]  Anthony G. Cohn,et al.  Qualitative Spatial Representation and Reasoning Techniques , 1997, KI.

[56]  Brandon Bennett,et al.  Logical representations for automated reasoning about spatial relationships , 1997 .

[57]  Ian Pratt-Hartmann,et al.  A Complete Axiom System for Polygonal Mereotopology of the Real Plane , 1998, J. Philos. Log..

[58]  Ian Horrocks,et al.  Using an Expressive Description Logic: FaCT or Fiction? , 1998, KR.

[59]  Gérard Ligozat,et al.  Reasoning about Cardinal Directions , 1998, J. Vis. Lang. Comput..

[60]  Anthony G. Cohn,et al.  Connection Relations in Mereotopology , 1998, ECAI.

[61]  Christoph Dornheim.  Undecidability of Plane Polygonal Mereotopology , 1998, KR.

[62]  Volker Haarslev,et al.  Foundations of Spatioterminological Reasoning with Description Logics , 1998, KR.

[63]  Philippe Muller,et al.  A Qualitative Theory of Motion Based on Spatio-Temporal Primitives , 1998, KR.

[64]  Bernhard Nebel,et al.  On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus , 1999, Artif. Intell..

[65]  Jochen Renz,et al.  Maximal Tractable Fragments of the Region Connection Calculus: A Complete Analysis , 1999, IJCAI.

[66]  Roberto Casati,et al.  Parts and Places: The Structures of Spatial Representation , 1999 .

[67]  Maarten Marx,et al.  Undecidability of Compass Logic , 1999, J. Log. Comput..

[68]  Ian Horrocks,et al.  Practical Reasoning for Expressive Description Logics , 1999, LPAR.

[69]  Valentin B. Shehtman,et al.  "Everywhere" and "Here" , 1999, J. Appl. Non Class. Logics.

[70]  Max J. Egenhofer,et al.  Identity-based change: a foundation for spatio-temporal knowledge representation , 2000, Int. J. Geogr. Inf. Sci..

[71]  Nils Klarlund,et al.  MONA Implementation Secrets , 2000, CIAA.

[72]  Frank Wolter,et al.  Spatial Reasoning in RCC-8 with Boolean Region Terms , 2000, ECAI.

[73]  Ullrich Hustadt,et al.  MSPASS: Modal Reasoning by Translation and First-Order Resolution , 2000, TABLEAUX.

[74]  John G. Stell,et al.  Boolean connection algebras: A new approach to the Region-Connection Calculus , 2000, Artif. Intell..

[75]  Frank Wolter,et al.  Decidable fragment of first-order temporal logics , 2000, Ann. Pure Appl. Log..

[76]  A. Galton.  Qualitative Spatial Change , 2001 .

[77]  Anthony G. Cohn,et al.  Qualitative Spatial Representation and Reasoning: An Overview , 2001, Fundam. Informaticae.

[78]  Christian Günsel,et al.  Towards an Implementation of the Temporal Description Logic TLALC , 2001, Description Logics.

[79]  Michael Fisher,et al.  Towards First-Order Temporal Resolution , 2001, KI/ÖGAI.

[80]  Frank Wolter,et al.  A Note on Concepts and Distances , 2001, Description Logics.

[81]  Frank Wolter,et al.  Monodic fragments of first-order temporal logics: 2000-2001 A.D , 2001, LPAR.

[82]  Patrick Blackburn.  Fine Grained Theories of Time , 2001 .

[83]  Michael Zakharyaschev,et al.  On the Products of Linear Modal Logics , 2001, J. Log. Comput..

[84]  Marco Aiello,et al.  A Spatial Similarity Measure based on Games: Theory and Practice , 2002, Log. J. IGPL.

[85]  Mark Reynolds,et al.  Axioms for Branching Time , 2002, J. Log. Comput..

[86]  J. Benthem,et al.  Logical Patterns in Space , 2002 .

[87]  Jochen Renz,et al.  A Canonical Model of the Region Connection Calculus , 1997, J. Appl. Non Class. Logics.

[88]  Jean-François Condotta,et al.  Computational Complexity of Propositional Linear Temporal Logics Based on Qualitative Spatial or Temporal Reasoning , 2002, FroCoS.

[89]  R. Thomason.  Combinations of Tense and Modality , 2002 .

[90]  Frank Wolter,et al.  Connecting Abstract Description Systems , 2002 .

[91]  Mark Reynolds,et al.  The complexity of the temporal logic with "until" over general linear time , 2003, J. Comput. Syst. Sci..

[92]  D. Gabbay,et al.  Many-Dimensional Modal Logics: Theory and Applications , 2003 .

[93]  Andrzej Grzegorczyk,et al.  Axiomatizability of geometry without points , 1960, Synthese.

[94]  Anthony G. Cohn,et al.  Multi-Dimensional Modal Logic as a Framework for Spatio-Temporal Reasoning , 2002, Applied Intelligence.