Qualitative Spatial Representation and Reasoning Techniques

The field of Qualitative Spatial Reasoning is now an active research area in its own right within AI (and also in Geographical Information Systems) having grown out of earlier work in philosophical logic and more general Qualitative Reasoning in AI. In this paper (which is an updated version of [25]) I will survey the state of the art in Qualitative Spatial Reasoning, covering representation and reasoning issues as well as pointing to some application areas.

[1]  Nicholas Mark Gotts,et al.  How Far Can We 'C'? Defining a 'Doughnut' Using Connection Alone , 1994, KR.

[2]  M. Knauff,et al.  Preferred mental models in qualitative spatial reasoning: A cognitive assessment of Allen's calculus , 1995 .

[3]  Annette Herskovits,et al.  Language and spatial cognition , 1986 .

[4]  Giangiacomo Gerla Chapter 18 – Pointless Geometries , 1995 .

[5]  Anthony G. Cohn,et al.  Qualitative Simulation Based on a Logical Formalism of Space and Time , 1992, AAAI.

[6]  Volker Haarslev,et al.  A fully formalized theory for describing visual notations , 1998 .

[7]  B. L. Clark Individuals and points. , 1985 .

[8]  Geoffrey Edwards The Voronoi Model and Cultural Space: Applications to the Social Sciences and Humanities , 1993, COSIT.

[9]  Anthony G. Cohn,et al.  Conceptual Neighbourhoods in Temporal and Spatial Reasoning , 1994 .

[10]  Louis J. Hoebel,et al.  Book review: Readings in Planning Edited by James Allen, James Hendler, and Austin Tate (Morgan Kaufmann, San Mateo, CA, 1990) , 1991, SGAR.

[11]  Anthony G. Cohn,et al.  Calculi for Qualitative Spatial Reasoning , 1996, AISMC.

[12]  Jérôme Lang,et al.  When Nonmonotonicity Comes from Distances , 1994, KI.

[13]  Giangiacomo Gerla,et al.  Connection Structures: Grzegorczyk's and Whitehead's Definitions of Point , 1996, Notre Dame J. Formal Log..

[14]  Olivier Raiman,et al.  Order of Magnitude Reasoning , 1986, Artif. Intell..

[15]  Jayant Sharma,et al.  Topological Relations Between Regions in R² and Z² , 1993, SSD.

[16]  Joseph Henry Woodger,et al.  The axiomatic method in biology , 1938 .

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

[18]  A. Cohn,et al.  A connection based approach to common-sense topological description and reasoning , 1996 .

[19]  James A. Hendler,et al.  Readings in Planning , 1994 .

[20]  M. Egenhofer,et al.  Topological Relations Between Regions in IR 2 and ZZ 2 * , 1993 .

[21]  Max J. Egenhofer,et al.  On the Equivalence of Topological Relations , 1995, Int. J. Geogr. Inf. Sci..

[22]  Boi Faltings,et al.  Qualitative Spatial Reasoning Using Algebraic Topology , 1995, COSIT.

[23]  Jack Sklansky,et al.  Measuring Concavity on a Rectangular Mosaic , 1972, IEEE Transactions on Computers.

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

[25]  Kai Zimmermann,et al.  Measuring without Measures: The Delta-Calculus , 1995, COSIT.

[26]  Antony Galton Taking Dimension Seriously in Qualitative Spatial Reasoning , 1996, ECAI.

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

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

[29]  Amitabha Mukerjee,et al.  A Qualitative Model for Space , 1990, AAAI.

[30]  Andrew U. Frank,et al.  Qualitative spatial reasoning about distances and directions in geographic space , 1992, J. Vis. Lang. Comput..

[31]  Andrew U. Frank,et al.  Spatial Information Theory A Theoretical Basis for GIS , 1993, Lecture Notes in Computer Science.

[32]  A. Cohn,et al.  Visual Language Syntax and Semantics: a Spatial Logic Approach , 1996 .

[33]  Andrew U. Frank,et al.  Qualitative Spatial Reasoning with Cardinal Directions , 1991, ÖGAI.

[34]  A. Cohn A Mereological Approach to Representing Spatial Vagueness , 1994 .

[35]  Antony Galton,et al.  Towards a Qualitative Theory of Movement , 1995, COSIT.

[36]  D. Randell,et al.  Exploiting lattices in a theory of space and time , 1992 .

[37]  Anthony G. Cohn,et al.  The ‘Egg-Yolk’ Representation of Regions with Indeterminate Boundaries , 2020 .

[38]  Eliseo Clementini,et al.  A Global Framework for Qualitative Shape Description , 1997, GeoInformatica.

[39]  Mark Gahegan,et al.  Proximity Operators for Qualitative Spatial Reasoning , 1995, COSIT.

[40]  John A. Barnden,et al.  Semantic Networks , 1998, Encyclopedia of Social Network Analysis and Mining.

[41]  Boi Faltings,et al.  Qualitative Kinematics: A Framework , 1987, IJCAI.

[42]  Murray Shanahan,et al.  Default Reasoning about Spatial Occupancy , 1995, Artif. Intell..

[43]  Bowman L. Clarke,et al.  Individuals and points , 1985, Notre Dame J. Formal Log..

[44]  Volker Haarslev Formal semantics of visual languages using spatial reasoning , 1995, Proceedings of Symposium on Visual Languages.

[45]  P. N. Johnson-Laird Language and spatial cognition: an interdisciplinary study of prepositions in English: by Annette Herskovits, Cambridge: Cambridge University Press, 1986 , 1989 .

[46]  Roberto Casati,et al.  Philosophy and the Cognitive Sciences: Proceedings of the 16th International Wittgenstein Symposium, 15-22 August 1993, Kirchberg Am Wechsel (Austria) , 1994 .

[47]  Benjamin Kuipers,et al.  Navigation and Mapping in Large Scale Space , 1988, AI Mag..

[48]  Anthony G. Cohn,et al.  The EGG/YOLK reliability hierarchy: semantic data integration using sorts with prototypes , 1994, CIKM '94.

[49]  Eliseo Clementini,et al.  Approximate topological relations , 1997, Int. J. Approx. Reason..

[50]  Monika Lundell A Qualitative Model of Gradient Flow in a Spatially Distributed Parameter , 1995 .

[51]  Christoph Schlieder,et al.  Representing Visible Locations for Qualitative Navigation , 1993 .

[52]  N. Gotts An Axiomatic Approach to Topology For Spatial Information Systems , 1996 .

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

[54]  Anthony G. Cohn,et al.  Representing and Reasoning with Qualitative Spatial Relations About Regions , 1997 .

[55]  Anthony G. Cohn,et al.  Spatial Regions with Undetermined Boundaries , 1994 .

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

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

[58]  David M. Mark,et al.  The 9-Intersection: Formalism and Its Use for Natural-Language Spatial Predicates (94-1) - eScholarship , 1994 .

[59]  Daniel R. Montello,et al.  Spatial Information Theory A Theoretical Basis for GIS , 1995, Lecture Notes in Computer Science.

[60]  Anthony G. Cohn,et al.  Computing Transivity Tables: A Challenge For Automated Theorem Provers , 1992, CADE.

[61]  Carola Eschenbach,et al.  Classical mereology and restricted domains , 1995, Int. J. Hum. Comput. Stud..

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

[63]  Brandon Bennett,et al.  Carving Up Space: Steps Towards Construction of an Absolutely Complete Theory of Spatial Regions , 1996, JELIA.

[64]  R. Pollack,et al.  Allowable Sequences and Order Types in Discrete and Computational Geometry , 1993 .

[65]  T. Topaloglou First-order Theories of Approximate Space Extended Abstract , 1994 .

[66]  Achille C. Varzi Spatial Reasoning in a Holey World , 1993, AI*IA.

[67]  B. Bennett,et al.  When does a Composition Table Provide a Complete and TractableProof Procedure for a Relational Constraint Language ? , 1997 .

[68]  Daniel R. Montello,et al.  Scale and Multiple Psychologies of Space , 1993, COSIT.

[69]  Max J. Egenhofer,et al.  Advances in Spatial Databases , 1997, Lecture Notes in Computer Science.

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

[71]  Cornelia Zelinsky-Wibbelt The Semantics of prepositions : from mental processing to natural language processing , 1993 .

[72]  Max J. Egenhofer,et al.  Reasoning about Gradual Changes of Topological Relationships , 1992, Spatio-Temporal Reasoning.

[73]  Wesley A. Mah,et al.  Cognitive reference points in judgments of symbolic magnitude , 1982, Cognitive Psychology.

[74]  Eliseo Clementini,et al.  A Small Set of Formal Topological Relationships Suitable for End-User Interaction , 1993, SSD.

[75]  Giangiacomo Gerla,et al.  Connection Structures , 1991, Notre Dame J. Formal Log..

[76]  Raman Rajagopalan A Model for Integrated Qualitative Spatial and Dynamic Reasoning about Physical Systems , 1994, AAAI.

[77]  Christoph Schlieder,et al.  Reasoning About Ordering , 1995, COSIT.

[78]  Kai Zimmermann,et al.  Enhancing Qualitative Spatial Reasoning - Combining Orientation and Distance , 1993, COSIT.

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

[80]  Anthony G. Cohn,et al.  Qualitative Reasoning , 1987, Advanced Topics in Artificial Intelligence.

[81]  Boi Faltings,et al.  A Symbolic Approach to Qualitative Kinematics , 1992, Artif. Intell..

[82]  T. D. Laguna Point, Line, and Surface, as Sets of Solids , 1922 .

[83]  Erland Jungert Symbolic Spatial Reasoning on Object Shapes for Qualitative Matching , 1993, COSIT.

[84]  Bernhard Nebel,et al.  Computational Properties of Qualitative Spatial Reasoning: First Results , 1995, KI.

[85]  Achille C. Varzi Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology , 1996, Data Knowl. Eng..

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

[87]  Anthony G. Cohn,et al.  Taxonomies of logically defined qualitative spatial relations , 1995, Int. J. Hum. Comput. Stud..

[88]  Anthony G. Cohn,et al.  A Hierarchical Representation of Qualitative Shape based on Connection and Convexity , 1995, COSIT.

[89]  Daniel Hernández,et al.  Qualitative Representation of Spatial Knowledge , 1994, Lecture Notes in Computer Science.

[90]  Eliseo Clementini,et al.  Qualitative Representation of Positional Information , 1997, Artif. Intell..

[91]  Nicola Guarino,et al.  A Pointless Theory of Space Based on Strong Connection and Congruence , 1996, KR.

[92]  Anthony G. Cohn,et al.  Transition-based Qualitative Simulation , 1996 .

[93]  David M. Mark,et al.  Evaluating and Refining Computational Models of Spatial Relations Through Cross-Linguistic Human-Subjects Testing , 1995, COSIT.

[94]  M. Brady Criteria for Representations of Shape , 1983 .

[95]  James A. Hendler,et al.  A Review of AI Planning Techniques , 1990 .

[96]  Antony Galton,et al.  Towards an Integrated Logic of Space, Time and Motion , 1993, IJCAI.

[97]  Luis Fariñas del Cerro,et al.  Modal Logics for Incidence Geometries , 1997, J. Log. Comput..

[98]  Michael Leyton,et al.  A Process-Grammar for Shape , 1988, Artif. Intell..

[99]  M. Aurnague,et al.  A three-level approach to the semantics of space , 1993 .

[100]  Achille C. Varzi,et al.  Holes and Other Superficialities , 1994 .

[101]  Jonathan H. Fernyhough Event Recognition using Qualitative Reasoning on Automatically Generated Spatio-Temporal Models from , 1997 .

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

[103]  Donald D. Hoffman,et al.  Codon constraints on closed 2D shapes , 1985, Computer Vision Graphics and Image Processing.

[104]  Ralf Röhrig,et al.  A Theory for Qualitative Spatial Reasoning Based on Order Relations , 1994, AAAI.

[105]  L. Vieu Semantique des relations spatiales et inferences spatio-temporelles : une contribution a l'etude des structures formelles de l'espace en langage naturel , 1991 .

[106]  Zhan Cui,et al.  Naive topology: modeling the force pump , 1993 .

[107]  N. Gotts Deening a `doughnut' Made Diicult , 1994 .

[108]  Requicha,et al.  Solid Modeling: A Historical Summary and Contemporary Assessment , 1982, IEEE Computer Graphics and Applications.

[109]  Nicholas Mark GottsDivision Formalizing Commonsense Topology : The INCH Calculus , 1996 .

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

[111]  P. D. Felice,et al.  A comparison of methods for representing topological relationships , 1995 .

[112]  Jayant Sharma,et al.  Modeling Topological Spatial Relations: Strategies for Query Processing , 1998 .

[113]  Patrick J. Hayes,et al.  The Naive Physics Manifesto , 1990, The Philosophy of Artificial Intelligence.

[114]  G. Stephanopoulos,et al.  Formal order-of-magnitude reasoning in process engineering , 1989 .

[115]  Laurent Siklóssy Generalized means-ends analysis and artificial intelligence , 1971, Inf. Sci..

[116]  Barry Smith Ontology and the logistic analysis of reality , 1993 .

[117]  Anthony G. Cohn,et al.  A Comparison Of Structures In Spatial And Temporal Logics , 1994 .

[118]  Oliver Lemon,et al.  Ontologies for Plane, Polygonal Mereotopology , 1997, Notre Dame J. Formal Log..

[119]  Max J. Egenhofer,et al.  A Formal Definition of Binary Topological Relationships , 1989, FODO.

[120]  Anthony G. Cohn,et al.  Qualitative Spatial Representation and Reasoning with the Region Connection Calculus , 1997, GeoInformatica.

[121]  Stephen G. Kaufman A Formal Theory of Spatial Reasoning , 1991, KR.

[122]  Christian Freksa,et al.  Temporal Reasoning Based on Semi-Intervals , 1992, Artif. Intell..

[123]  Boi Faltings,et al.  Recent advances in qualitative physics , 1993 .

[124]  Peter Struss,et al.  Qualitative Reasoning , 1997, The Computer Science and Engineering Handbook.

[125]  Max J. Egenhofer,et al.  Topological Relations Between Regions with Holes , 1994, Int. J. Geogr. Inf. Sci..

[126]  Anthony G. Cohn,et al.  Modelling Topological and Metrical Properties in Physical Processes , 1989, KR.