Skip to main content

Qualitative spatial representation and reasoning techniques

  • Invited Talks
  • Conference paper
  • First Online:
KI-97: Advances in Artificial Intelligence (KI 1997)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1303))

Included in the following conference series:

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J F Allen. Maintaining knowledge about temporal intervals. Communications of the ACM, 26(11):832–843, 1983.

    Google Scholar 

  2. N Asher and J Lang. When nonmonotonicity comes from distance. In L Nebel, B and Dreschler-Fischer, editor, KI-94: Advances in Artificial Intelligence, pages 308–318. Springer-Verlag, 1994.

    Google Scholar 

  3. N Asher and L Vieu. Toward a geometry of common sense: A semantics and a complete axiomatization of mereotopology. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI-95), Montreal, 1995.

    Google Scholar 

  4. M Aurnague and L Vieu. A three-level approach to the semantics of space. In C Zelinsky-Wibbelt, editor, The semantics of prepositions — from mental processing to natural language processing, Berlin, 1993. Mouton de Gruyter.

    Google Scholar 

  5. B Balbiani, V Dugat, L Farnmas del Cerro, and A Lopez. Eléments de géométrie mécanique. Editions Hermes, 1994.

    Google Scholar 

  6. P Balbiani, L Del Cerro, T Tinchev, and D Vakarelov. Modal logics for incidence geometries. J. Logic and Computation, 1:59–78, 1997.

    Google Scholar 

  7. B. Bennett. Spatial reasoning with propositional logics. In J Doyle, E Sandewall, and P Torasso, editors, Principles of Knowledge Representation and Reasoning; Proceedings of the 4th International Conference (KR94), San Francisco, CA., 1994. Morgan Kaufmann.

    Google Scholar 

  8. B Bennett. Carving up space: steps towards construction of an absolutely complete theory of spatial regions. In L.M. Pereira J.J. Alfres and E. Orlowska, editors, Proceedings of JELIA'96, pages 337–353, 1996.

    Google Scholar 

  9. B Bennett. Modal logics for qualitative spatial reasoning. Bulletin of the Interest Group in Pure and Applied Logic (IGPL), 1996.

    Google Scholar 

  10. B Bennett, A Isli, and A G Cohn. When does a composition table provide a complete and tractable proof procedure for a relational constraint language? In Proceedings of the IJCAI-97 workshop on Spatial and Temporal Reasoning, Nagoya, Japan, 1997. to appear.

    Google Scholar 

  11. L. Biacino and G. Gerla. Connection structures. Notre Dame Journal of Formal Logic, 32(2), 1991.

    Google Scholar 

  12. S Borgo, N Guarino, and C Masolo. A pointless theory of space based on strong connecction and congruence. In Principles of Knowledge Representation and Reasoning, Pro 5th Conference, pages 220–229, 1996.

    Google Scholar 

  13. J M Brady. Criteria for representations of shape. Human and Machine Vision, 1993.

    Google Scholar 

  14. R Casati and A Varzi. Holes and Other Superficialities. MIT Press, Cambridge, MA, 1994.

    Google Scholar 

  15. B L Clarke. A calculus of individuals based on ‘connection'. Notre Dame Journal of Formal Logic, 23(3):204–218, July 1981.

    Google Scholar 

  16. B L Clarke. Individuals and points. Notre Dame Journal of Formal Logic, 26(1):61–75, 1985.

    Google Scholar 

  17. E Clementini and P Di Felice. A comparison of methods for representing topological relationships. Information Sciences, 3:149–178, 1995.

    Google Scholar 

  18. E Clementini and P Di Felice. An algebraic model for spatial objects with undetermined boundaries. In P Burrough and A M Frank, editors, Proceedings, GISDATA Specialist Meeting on Geographical Entities with Undetermined Boundaries,. Taylor Francis, 1996.

    Google Scholar 

  19. E Clementini and P Di Felice. Approximate topological relations. International Journal of Approximate Reasoning, 1997.

    Google Scholar 

  20. E Clementini and P Di Felice. A global framework for qualitative shape description. GeoInformatica, 1(1), 1997.

    Google Scholar 

  21. E Clementini, P Di Felice, and. D Hernández. Qualitative representation of positional information. Artificial Intelligence, 1997.

    Google Scholar 

  22. E Clementini, P Di Felice, and P Oosterom. A small set of formal topological relationships suitable for end user interatction. In D Abel and B C Ooi, editors, Proc. 3rd Int. Symp. on Large Spatial Databases, SSD, number 692 in LNCS, pages 277–295. Springer, 1994.

    Google Scholar 

  23. E Clementini, J Sharma, and M J Egenhofer. Modeling topological spatial relations: strategies for query processing. Computers and Graphics, 18(6):815–822, 1994.

    Google Scholar 

  24. A G Cohn. A hierarchcial representation of qualitative shape based on connection and convexity. In A Frank, editor, Proc COSIT95, LNCS, pages 311–326. Springer Verlag, 1995.

    Google Scholar 

  25. A G Cohn. Calculi for qualitative spatial reasoning. In J Pfalzgraf J Calmet, J A Campbell, editor, Artificial Intelligence and Symbolic Mathematical Computation, volume 1138 of LNCS, pages 124–143. Springer Verlag, 1996.

    Google Scholar 

  26. A G Cohn, B Bennett, J Gooday, and N Gotts. RCC: a calculus for region based qualitative spatial reasoning. Geoinformatica, to appear, 1997.

    Google Scholar 

  27. A G Cohn, B Bennett, J Gooday, and N Gotts. Representing and reasoning with qualitative spatial relations about regions. In O Stock, editor, Temporal and spatial reasoning. Kluwer, 1997. to appear.

    Google Scholar 

  28. A G Cohn, J M Gooday, and B Bennett. A comparison of structures in spatial and temporal logics. In R Casati, B Smith, and G White, editors, Philosophy and the Cognitive Sciences: Proceedings of the 16th International Wittgenstein Symposium, Vienna, 1994. Hölder-Pichler-Tempsky.

    Google Scholar 

  29. A G Cohn and N M Gotts. Spatial regions with undetermined boundaries. In Proceedings of Gaithesburg Workshop on GIS. ACM, December 1994.

    Google Scholar 

  30. A G Cohn and N M Gotts. A theory of spatial regions with indeterminate boundaries. In C. Eschenbach, C. Habel, and B. Smith, editors, Topological Foundations of Cognitive Science, 1994.

    Google Scholar 

  31. A G Cohn and N M Gotts. The ‘egg-yolk’ representation of regions with indeterminate boundaries. In P Burrough and A M Frank, editors, Proceedings, GISDATA Specialist Meeting on Geographical Objects with Undetermined Boundaries, pages 171–187. Francis Taylor, 1996.

    Google Scholar 

  32. A G Cohn and N M Gotts. A mereological approach to representing spatial vagueness. In J Doyle L C Aiello and S Shapiro, editors, Principles of Knowledge Representation and Reasoning, Proc. 5th Conference, pages 230–241. Morgan Kaufmann, 1996.

    Google Scholar 

  33. A G Cohn, D A Randell, and Z Cui. Taxonomies of logically defined qualitative spatial relations. Int. J of Human-Computer Studies, 43:831–846, 1995.

    Google Scholar 

  34. Z Cui, A G Cohn, and D A Randell. Qualitative simulation based on a logical formalism of space and time. In Proceedings AAAI-92, pages 679–684, Menlo Park, California, 1992. AAAI Press.

    Google Scholar 

  35. E Davis, N M Gotts, and A G Cohn. Constraint networks of topological relations and convexity. Technical report, Courant Institute, New York University, 1997.

    Google Scholar 

  36. T de Laguna. Point, line and surface as sets of solids. The Journal of Philosophy, 19:449–461, 1922.

    Google Scholar 

  37. C Dornheim. Vergleichende analyse topologischer ansaetze des qualitativen raeuml ichen siessens. Studienarbeit, fachereich informatik, Universitaet Hamburg, 1995.

    Google Scholar 

  38. G Edwards. The voronoi model and cultural space: Applications to the social sciences and humanities. In A U Frank and I Campari, editors, Spatial Information Theory: A Theoretical Basis for GIS, volume 716 of Lecture Notes in Computer Science, pages 202–214, Berlin, 1993. Springer Verlag.

    Google Scholar 

  39. M Egenhofer. A formal definition of binary topological relationships. In W. Litwin and H. Schek, editors, Third International Conference on Foundations of Data Organization and Algorithms (FODO) volume 367 of LNCS, pages 457–472. Springer Verlag, 1989.

    Google Scholar 

  40. M Egenhofer. Topological similarity. In Proc FISI workshop on the Toplogical Foundations of Cognitive Science, volume 37 of Reports of the Doctoral Series in Cognitive Science. University of Hamburg, 1994.

    Google Scholar 

  41. M Egenhofer and R Franzosa. Point-set topological spatial relations. International Journal of Geographical Information Systems, 5(2):161–174, 1991.

    Google Scholar 

  42. M Egenhofer and J Herring. Categorizing topological spatial relationships between point, line and area objects. In The 9-intersection: formalism and its use for natural language spatial predicates, Technical Report 94-1. National Center for Geographic Information and Analysis, Santa Barbara, 1994.

    Google Scholar 

  43. M Egenhofer and J Sharma. Topological relationships between regions in R 2 and Z 2. In D. Abel and B. C. Ooi, editors, Third International Symposium on Large Spatial Databases. Springer-Verlag, 1993.

    Google Scholar 

  44. M J Egenhofer and K K Al-Taha. Reasoning about gradual changes of topological relationships. In A U Frank, I Campari, and U Formentini, editors, Theories and Methods of Spatio-temporal Reasoning in Geographic Space, volume 639 of Lecture Notes in Computer Science, pages 196–219. Springer-Verlag, Berlin, 1992.

    Google Scholar 

  45. M J Egenhofer, E Clementini, and P Di Felice. Toplogical relations between regions with holes. Int. Journal of Geographical Information Systems, 8(2):129–144, 1994.

    Google Scholar 

  46. M J Egenhofer and R D Franzosa. On the equivalence of topological relations. International Journal of Geographical Information Systems, 9(2):133–152, 1995.

    Google Scholar 

  47. M J Egenhofer and D Mark. Naive geography. In A U Frank and W Kuhn, editors, Spatial Information Theory: a theoretical basis for GIS, volume 988 of Lecture Notes in Computer Science, pages 1–16. Springer-Verlag, Berlin, 1995.

    Google Scholar 

  48. C Eschenbach and W Heydrich. Classical mereology and restricted domains. Int. J. Human-Computer Studies, 43:723–740, 1995.

    Google Scholar 

  49. B. Faltings. A symbolic approach to qualitative kinematics. Artificial Intelligence, 52(2), 1992.

    Google Scholar 

  50. B Faltings. Qualitative spatial reaoning using algebraic topology. In A U Frank and W Kuhn, editors, Spatial Information Theory: a theoretical basis for GIS, volume 988 of Lecture Notes in Computer Science, pages 17–30, Berlin, 1995. Springer-Verlag.

    Google Scholar 

  51. B. Faltings and P. Struss, editors. Recent Advances in Qualitative Physics. MIT Press, Cambridge, Ma, 1992.

    Google Scholar 

  52. J Fernyhough, A G Cohn, and D C Hogg. Event recognition using qualitative reasoning on automatically generated spatio-temporal models from visual input. In Proc. IJCAI97 workshop on Spatial and Temporal Reasoning, 1997.

    Google Scholar 

  53. K Forbus, P Nielsen, and B Faltings. Qualitative kinematics: A framework. In Proceedings IJCAI-87, pages 430–436, 1987.

    Google Scholar 

  54. A Frank. Qualitative spatial reasoning with cardinal directions. Journal of Visual Languages and Computing, 3:343–371, 1992.

    Google Scholar 

  55. C Freksa. Temporal reasoning based on semi-intervals. Artificial Intelligence, 54:199–227, 1992.

    Google Scholar 

  56. H Fujihara and A Mukerjee. Qualitative reasoning about document design. Technical report, Texas A and M University, 1991.

    Google Scholar 

  57. M Gahegan. Proximity operators for qualitative spatial reasoning. In W Kuhn A Frank, editor, Spatial Information Theory: a theoretical basis for GIS, number 988 in Lecture Notes in Computer Science, pages 31–44, Berlin, 1995. Springer Verlag.

    Google Scholar 

  58. A Galton. Towards a qualitative theory of movement. In W Kuhn A Frank, editor, Spatial Information Theory: a theoretical basis for GIS, number 988 in Lecture Notes in Computer Science, pages 377–396, Berlin, 1995. Springer Verlag.

    Google Scholar 

  59. A Galton. Taking dimension seriously in qualitative spatial reasoning. In W. Wahlster, editor, Proceedings of the 12th European Conference on Artificial Intelligence, pages 501–505. John Wiley and Sons, 1996.

    Google Scholar 

  60. A P Galton. Towards an integrated logic of space, time and motion. In Proceedings IJCAI-93, Chambery, France, September 1993.

    Google Scholar 

  61. G. Gerla. Pointless geometries. In F. Buekenhout, editor, Handbook of Incidence Geometry, chapter 18, pages 1015–1031. Elsevier Science B.V., 1995.

    Google Scholar 

  62. J Glasgow, N H Narayanan, and B Chandrasekara. Diagrammatic Reasoning. MIT Press, 1995.

    Google Scholar 

  63. J Gooday and A G Cohn. Transition-based qualitative simulation. In Proceeding of the 10th International Workshop on Qualitative Reasoning, pages 74–82. AAAI press, 1996.

    Google Scholar 

  64. J Gooday and A G Cohn. Visual language syntax and semantics: A spatial logic approach. In K Marriott and B Meyer, editors, Proc Workshop on Theory of Visual Languages, Gubbio, Italy, 1996.

    Google Scholar 

  65. J M Gooday and A G Cohn. Using spatial logic to describe visual languages. Artificial Intelligence Review, 10(1–2), 1995. This paper also appears in Integration of Natural Language and Vision Processing (Vol. IV), ed P MckEvitt, Kluwer, 1996.

    Google Scholar 

  66. J Goodman and R Pollack. Allowable sequences and order types in discrete and computational geometry. In J Pach, editor, New trends in discrete and computational geometry, pages 103–134. Springer Verlag, 1993.

    Google Scholar 

  67. N M Gotts. Defining a ‘doughnut’ made difficult. In C. Eschenbach, C. Habel, and B. Smith, editors, Topological Foundations of Cognitive Science, volume 37 of Reports of the Doctoral programme in Cognitive Science. University of Hamburg, 1994.

    Google Scholar 

  68. N M Gotts. How far can we ‘C'? defining a ‘doughnut’ using connection alone. In J Doyle, E Sandewall, and P Torasso, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the 4th International Conference (KR94). Morgan Kaufmann, 1994.

    Google Scholar 

  69. N M Gotts. An axiomatic approach to topology for spatial information systems. Technical report, Report 96.25, School of Computer Studies, University of Leeds, 1996.

    Google Scholar 

  70. N M Gotts. Formalising commonsense topology: The inch calculus. In Proc. Fourth International Symposium on Artificial Intelligence and Mathematics, 1996.

    Google Scholar 

  71. N M Gotts. Toplogy from a single primitive relation: defining topological properties and relations in terms of connection. Technical report, Report 96.23, School of Computer Studies, University of Leeds, 1996.

    Google Scholar 

  72. N M Gotts. Using the RCC formalism to describe the topology of spherical regions. Technical report, Report 96.24, School of Computer Studies, University of Leeds, 1996.

    Google Scholar 

  73. N M Gotts, J M Gooday, and A G Cohn. A connection based approach to common-sense topological description and reasoning. The Monist, 79(1):51–75, 1996.

    Google Scholar 

  74. M. Grigni, D. Papadias, and C. Papadimitriou. Topological inference. In Proc. IJCAI-95, pages 901–906. Morgan Kaufmann, 1995.

    Google Scholar 

  75. A. Grzegorczyk. Undecidability of some topological theories. Fundamenta Mathematicae, 38:137–152, 1951.

    Google Scholar 

  76. H Guesgen and J Hertzberg. A constraint based approach to spatio-temporal reasoning. Applied Artificial Intelligence, 3:71–90, 1992.

    Google Scholar 

  77. V Haarslev. Formal semantics of visual languages using spatial reasoning. In Proceedings of the 11th IEEE Symposium on Visual Languages, 1995.

    Google Scholar 

  78. Volker Haarslev. A fully formalized theory for describing visual notations. In Proceedings of the AVI'96 post-conference Workshop on Theory of Visual Languages, Gubbio,Italy, May 1996.

    Google Scholar 

  79. P J Hayes. The naive physics manifesto. In D Mitchie, editor, Expert systems in the micro-electronic age. Edinburgh University Press, 1979.

    Google Scholar 

  80. D Hernández. Qualitative Representation of Spatial Knowledge, volume 804 of Lecture Notes in Artificial Intelligence. Springer-Verlag, 1994.

    Google Scholar 

  81. D Hernández, E Clementini, and P Di Felice. Qualitative distances. In W Kuhn A Frank, editor, Spatial Information Theory: a theoretical basis for GIS, number 988 in LNCS, pages 45–58, Berlin, 1995. Springer Verlag.

    Google Scholar 

  82. A Herskovits. Language and Spatial Cognition. An interdisciplinary study of prepositions in English. Cambridge University Press, 1986.

    Google Scholar 

  83. J Hobbs. Granularity. In Proceedings IJCAI-85, pages 432–435, 1985.

    Google Scholar 

  84. K. J. Holyoak and W. A. Mah. Cognitive reference points in judgments of symbolic magnitude. Cognitive Psychology, 14:328–352, 1982.

    Google Scholar 

  85. E. Jungert. Symbolic spatial reasoning on object shapes for qualitative matching. In A. U. Frank and L. Campari, editors, Spatial Information Theory: A Theoretical Basis for GIS, Lecture Notes in Computer Science No. 716, pages 444–462. COSIT'93, Springer-Verlag, 1993.

    Google Scholar 

  86. S Kaufman. A formal theory of spatial reasoning. In Proc Int. Conf. on Knowledge Representation and Reasoning, pages 347–356, 1991.

    Google Scholar 

  87. M Knauff, R Rauh, and C Schlieder. Preferred mental models in qualitative spatial reasoning: A cognitive assessment of Allen's calculus. In Proc. 17th Annual Conf. of the Cognitive Science Society, 1995.

    Google Scholar 

  88. B Kuipers. Qualitative Reasoning. MIT Press, Cambridge, MA., 1994.

    Google Scholar 

  89. B J Kuipers and T S Levitt. Navigating and mapping in large-scale space. AI Magazine, 9(2):25–43, 1988.

    Google Scholar 

  90. F Lehmann and A G Cohn. The EGG/YOLK reliability hierarchy: Semantic data integration using sorts with prototypes. In Proc. Conf. on Information Knowledge Management, pages 272–279. ACM Press, 1994.

    Google Scholar 

  91. M Leyton. A process grammar for shape. Artificial Intelligence, page 34, 1988.

    Google Scholar 

  92. G Ligozat. Towards a general characterization of conceptual neighbourhoods in temporal and spatial reasoning. In F D Anger and R Loganantharah, editors, Proceedings AAAI-94 Workshop on Spatial and Temporal Reasoning, 1994.

    Google Scholar 

  93. M Lundell. A qualitative model of gradient flow in a spatially distributed parameter. In Proc 9th Int. Workshop on Qualtiative Reasoning, Amsterdam, 1995.

    Google Scholar 

  94. D Mark, D Comas, M Egenhofer, S Freundschuh, J Gould, and J Nunes. Evaluating and refining computational models of spatial relations through crosslinguistic human-subjects testing. In W Kuhn A Frank, editor, Spatial Information Theory: a theoretical basis for GIS, number 988 in Lecture Notes in Computer Science, pages 553–568, Berlin, 1995. Springer Verlag.

    Google Scholar 

  95. M Mavrovouniotis and G Stephanopoulos. Formal order-of-magnitude reasoning in process engineering. Computers and Chemical Engineering, 12:867–881, 1988.

    Google Scholar 

  96. D Montello. Scale and multiple pyschologies of space. In I Campari A Frank, editor, Spatial Information Theory: a theoretical basis for GIS, number 716 in Lecture Notes in Computer Science, pages 312–321, Berlin, 1993. Springer Verlag.

    Google Scholar 

  97. A Mukerjee and G Joe. A qualitative model for space. In Proceedings AAAI-90, pages 721–727, Los Altos, 1990. Morgan Kaufmann.

    Google Scholar 

  98. B. Nebel. Computational properties of qualitative spatial reasoning: First results. In Procedings of the 19th German AI Conference, 1995.

    Google Scholar 

  99. B Nebel. Reasoning about temporal relations: a maximal tractable subset of Allen's interval algebra. Journal of the Association for Computing Machinery, 42(1):43–66, January 1995.

    Google Scholar 

  100. I Pratt and O Lemon. Ontologies for plane, polygonal mereotopology. Technical Report UMCS-97-1-1, Univ. of Manchester, Dept of Computer Science, 1997.

    Google Scholar 

  101. Ian Pratt and Dominik Schoop. A complete axiom system for polygonal mereotopology of the plane. Technical Report UMCS-97-2-2, University of Manchester, 1997.

    Google Scholar 

  102. O Raiman. Order of magnitude reasoning. In AAAI-86: Proceedings of the National Conference on AI, pages 100–104, 1996.

    Google Scholar 

  103. R Rajagopalan. A model for integrated qualitative spatial and dynamic reasoning about physical systems. In Proc. AAAI, pages 1411–1417, 1994.

    Google Scholar 

  104. C G Ralha. A Framework for Dynamic Structuring of Information. PhD thesis, School of Computer Studies, Universities of Leeds, 1996.

    Google Scholar 

  105. D A Randell and A G Cohn. Exploiting lattices in a theory of space and time. Computers and Mathematics with Applications, 23(6-9):459–476, 1992. Also appears in “Semantic Networks”, ed. F. Lehmann, Pergamon Press, Oxford, pp. 459–476, 1992.

    Google Scholar 

  106. D A Randell, A G Cohn, and Z Cui. Computing transitivity tables: A challenge for automated theorem provers. In Proceedings CADE 11, Berlin, 1992. Springer Verlag.

    Google Scholar 

  107. D A Randell, A G Cohn, and Z Cui. Naive topology: Modelling the force pump. In P Struss and B Faltings, editors, Advances in Qualitative Physics, pages 177–192. MIT Press, 1992.

    Google Scholar 

  108. D A Randell, Z Cui, and A G Cohn. A spatial logic based on regions and connection. In Proc. 3rd Int. Conf. on Knowledge Representation and Reasoning, pages 165–176, San Mateo, 1992. Morgan Kaufmann.

    Google Scholar 

  109. D.A. Randell and A.G. Cohn. Modelling topological and metrical properties of physical processes. In R Brachman, H Levesque, and R Reiter, editors, Proceedings 1st International Conference on the Principles of Knowledge Representation and Reasoning, pages 55–66, Los Altos, 1989. Morgan Kaufmann.

    Google Scholar 

  110. Jochen Renz and Bernhard Nebel. On the complexity of qualitative spatial reasoning: a maximal tractable fragment of the Region Connection Calculus. In Proceedings of IJCAI-97, 1997.

    Google Scholar 

  111. A A G Requicha and H B Boelcke. Solid modelling: a historical summary aand contemporary assessment. IEEE Computer Graphics and Applications, 2:9–24, 1992.

    Google Scholar 

  112. W Richards and D Hoffman. Codon constraints on closed 2d shapes. Computer Vision, graphics and impage processing, 31:265–281, 1985.

    Google Scholar 

  113. R Röhrig. A theory for qualitative spatial reasoning based on order relations. In AAAI-94: Proceedings of the 12th National Conference on AI, volume 2, pages 1418–1423, Seattle, 1994.

    Google Scholar 

  114. C Schlieder. Representing visible locations for qualitative navigation. In N Piera Carreté and M G Singh, editors, Qualitative Reasoning and Decision Technologies, pages 523–532, Barcelona, 1993. CIMNE.

    Google Scholar 

  115. C Schlieder. Reasoning about ordering. In W Kuhn A Frank, editor, Spatial Information Theory: a theoretical basis for GIS, number 988 in Lecture Notes in Computer Science, pages 341–349, Berlin, 1995. Springer Verlag.

    Google Scholar 

  116. C Schlieder. Qualitative shape representation. In P Burrough and A M Frank, editors, Proceedings, GISDATA Specialist Meeting on Geographical Objects with Undetermined Boundaries. Francis Taylor, 1996.

    Google Scholar 

  117. M Shanahan. Default reasoning about spatial occupancy. Artificial Intelligence, 1995.

    Google Scholar 

  118. J Sklansky. Measuring concavity on a rectangular mosaic. IEEE Trans. on Computers, C-21(12):1355–1364, 1972.

    Google Scholar 

  119. B Smith. Ontology and the logicistic analysis of reality. In N Guarino and R Poli, editors, Proceedings International Workshop on Formal Ontology in Conceptual Analysis and Knowledge Representation, 1993. Revised version forthcoming in G Haefliger and P M Simons, eds, Analytic Phenomenology, Kluwer.

    Google Scholar 

  120. B Smith. Mereotopology: A theory of parts and boundaries. Data and Knowledge Engineering, 20(3):287–303, November 1996.

    Google Scholar 

  121. J. G. Stell and M. F. Worboys. The algebraic structure of sets of regions. In Proc COSIT97, LNCS. Springer Verlag, 1997.

    Google Scholar 

  122. A. Tarski. Foundations of the geometry of solids. In Logic, Semantics, Metamathematics, chapter 2. Oxford Clarendon Press, 1956. trans. J.H. Woodger.

    Google Scholar 

  123. A Tate, J Hendler, and M Drummond. A review of Al planning techniques. In J Allen, J Hendler, and A Tate, editors, Readings in Planning. Morgan Kaufman, San Mateo, CA, 1990.

    Google Scholar 

  124. T Topaloglou. First order theories of approximate space. In F Anger et al., editor, Working notes of AAAI workshop on spatial and temporal reasoning, pages 283–296, Seattle, 1994.

    Google Scholar 

  125. A Varzi. On the boundary between mereology and topology. In R Casati, B Smith, and G White, editors, Philosophy and the Cognitive Sciences: Proceedings of the 16th International Wittgenstein Symposium. Hölder-Pichler-Tempsky, Vienna, 1994.

    Google Scholar 

  126. A Varzi. Parts, wholes, and part-whole relations: the prospects of mereotopology. Data and Knowledge Engineering, 20(3):259–286, 1996.

    Google Scholar 

  127. A C Varzi. Spatial reasoning in a holey world. In Proceedings of the Spatial and Temporal Reasoning workshop, IJCAI-93, pages 47–59, 1993.

    Google Scholar 

  128. L Vieu. Sémantigue des relations spatiales et inferences spatio-temporelles. PhD thesis, University Paul Sabatier, Toulouse, 1991.

    Google Scholar 

  129. D S Weld and J De Kleer, editors. Readings in Qualitative Reasoning About Physical Systems. Morgan Kaufman, San Mateo, Ca, 1990.

    Google Scholar 

  130. A N Whitehead. Process and Reality. The Macmillan Company, New York, 1929.

    Google Scholar 

  131. A N Whitehead. Process and reality: corrected edition. The Free Press, Macmillan Pub. Co., New York, 1978. edited by D.R. Griffin and D.W. Sherburne.

    Google Scholar 

  132. J.H. Woodger. The Axiomatic Method in Biology. Cambridge University Press, 1937.

    Google Scholar 

  133. K Zimmermann. Enhancing qualitative spatial reasoning-combining orientation and distance. In I Campari A Frank, editor, Spatial Information Theory: a theoretical basis for GIS, number 716 in Lecture Notes in Computer Science, pages 69–76, Berlin, 1993. Springer Verlag.

    Google Scholar 

  134. K Zimmermann. Measuring without distances: the delta calculus. In W Kuhn A Frank, editor, Spatial Information Theory: a theoretical basis for GIS, number 988 in Lecture Notes in Computer Science, pages 59–68, Berlin, 1995. Springer Verlag.

    Google Scholar 

  135. K Zimmermann and C Freksa. Enhancing spatial reasoning by the concept of motion. In A Sloman, editor, Prospects for Artificial Intelligence, pages 140–147. IOS Press, 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Gerhard Brewka Christopher Habel Bernhard Nebel

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cohn, A.G. (1997). Qualitative spatial representation and reasoning techniques. In: Brewka, G., Habel, C., Nebel, B. (eds) KI-97: Advances in Artificial Intelligence. KI 1997. Lecture Notes in Computer Science, vol 1303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3540634932_1

Download citation

  • DOI: https://doi.org/10.1007/3540634932_1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63493-5

  • Online ISBN: 978-3-540-69582-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics