The Egenhofer–Cohn Hypothesis or, Topological Relativity?

  • Alexander KlippelEmail author
  • Rui Li
  • Jinlong Yang
  • Frank Hardisty
  • Sen Xu
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)


In this chapter, we provide an overview of research on cognitively validating qualitative calculi, focusing on the region connection calculus (RCC) and Egenhofer’s intersection models (IM). These topological theories are often claimed to be foundational to spatial cognition, a concept we term the EgenhoferCohn Hypothesis. (The authors are aware of the limitations of the chosen title/term. Neither Egenhofer nor Cohn necessarily support this claim in a strong form but they kindly agreed to have their names used here. Additionally, there are other approaches to topology, Cohn is the third author on the classic RCC paper, and Egenhofer published his work with co-authors. However, we feel that these two names best summarize the two most prominent topological theories in the spatial sciences.) We have been particularly interested in extending existing approaches into the realm of spatio-temporal representation and reasoning. We provide an overview on a series of experiments that we conducted to shed light on geographic event conceptualization and topology’s role in modeling and explaining cognitive behavior. Our framework also incorporates approaches to visually analyze cognitive behavior, allowing for interactive and in-depth analyses of cognitive conceptualizations. We present tangible results that can be distilled from generalizing from several experiments. These results show that the strong version of the Egenhofer–Cohn Hypothesis is not supported by all results; we suggest amendments to topological relationship specifications that are needed to serve as a sufficient basis for bridging formal and observed human spatial cognitive processes. We term this approach topological relativity.


Topology Spatial knowledge Qualitative spatial reasoning 


  1. Abler R, Adams JS, Gould P (1971) Spatial organization: the geographer’s view of the world. Prentice-Hall, Englewood CliffsGoogle Scholar
  2. Alexandroff P (1961) Elementary concepts of topology. Dover Publications, New YorkGoogle Scholar
  3. Allen JF (1983) Maintaining knowledge about temporal intervals. Commun ACM 26(11):832–843CrossRefGoogle Scholar
  4. Barsalou LW (2008) Grounded cognition. Annu Rev Psychol 59:617–645CrossRefGoogle Scholar
  5. Braitenberg V (1984) Vehicles. Experiments in synthetic psychology. MIT Press, CambridgeGoogle Scholar
  6. Bruns HT, Egenhofer MJ (1996) Similarity of spatial scenes. In: Kraak MJ, Molenaar M (eds) Seventh international symposium on spatial data handling (SDH’96), Delft, The Netherland. Taylor & Francis, London and New York, pp 173–184Google Scholar
  7. Chater N (1999) The search for simplicity: a fundamental cognitive principle. Q J Exp Psychol 52A(2):273–302Google Scholar
  8. Clementini E, Di Felice P, van Oosterom P (1993) A small set of formal topological relationships suitable for end-user interaction. In: Abel D, Ooi BC (eds) Advances in spatial databases. Proceedings of the third international symposium, SSD ‘93 Singapore, 23–25 June 1993. Springer, Berlin, pp 277–295Google Scholar
  9. Cohn AG, Renz J (2008) Qualitative spatial representation and reasoning. In: van Harmelen F, Lifschitz V, Porter B (eds) Foundations of artificial intelligence. Handbook of knowledge representation, 1st edn. Elsevier, Amsterdam, pp 551–596Google Scholar
  10. Cui Z, Cohn AG, Randell DA (1992) Qualitative simulation based on a logical formalism of space and time. In: Proceedings AAAI-92. AAAI Press, Menlo Park, pp 679–684Google Scholar
  11. Egenhofer MJ (2010) The family of conceptual neighborhood graphs for region–region relations. In: Fabrikant SI, Reichenbacher T, van Krefeld M, Schlieder C (eds) Proceedings of sixth international conference, GIScience 2010 Zürich, Switzerland, 14–17 Sep 2010. Springer, Berlin, pp 42–55Google Scholar
  12. Egenhofer MJ, Al-Taha KK (1992) Reasoning about gradual changes of topological relationships. In: Frank AU, Campari I, Formentini U (eds) Theories and methods of spatio-temporal reasoning in geographic space. Springer, Berlin, pp 196–219CrossRefGoogle Scholar
  13. Egenhofer MJ, Franzosa RD (1991) Point-set topological spatial relations. Int J Geogr Inf Syst 5(2):161–174CrossRefGoogle Scholar
  14. Egenhofer MJ, Mark DM (1995a) Modeling conceptual neighborhoods of topological relations. Int J Geogr Inf Syst 9(5):555–565CrossRefGoogle Scholar
  15. Egenhofer MJ, Mark DM (1995b) Naive geography. In: Frank AU, Kuhn W (eds) Spatial information theory. A theoretical basis for GIS. Proceedings of international conference, COSIT 95, Semmering, Austria, 21–23 Sept 1995. Springer, Berlin, pp 1–15Google Scholar
  16. Egenhofer MJ, Shariff AR (1998) Metric details for natural-language spatial relations. ACM Trans Inf Syst 16(4):295–321CrossRefGoogle Scholar
  17. Fabrikant SI, Hespanha SR, Hegarty M (2010) Cognitively inspired and perceptually salient graphic displays for efficient spatial inference making. Ann Assoc Am Geogr 100(1):13–29CrossRefGoogle Scholar
  18. Freksa C (1991) Qualitative spatial reasoning. In: Mark DM, Frank AU (eds) Cognitive and linguistic aspects of geographic space. Kluwer, Dordrecht, pp 361–372CrossRefGoogle Scholar
  19. Freksa C (1992) Temporal reasoning based on semi-intervals. Artif Intell 54(1):199–227CrossRefGoogle Scholar
  20. Freundschuh SM, Egenhofer MJ (1997) Human conceptions of spaces: implications for geographic information systems. Trans GIS 2(4):361–375CrossRefGoogle Scholar
  21. Galton A (1997) Continuous change in spatial regions. In: Hirtle SC, Frank AU (eds) Spatial information theory: a theoretical basis for GIS. Springer, Berlin, pp 1–14CrossRefGoogle Scholar
  22. Galton A (2000) Qualitative spatial change. Spatial information systems. Oxford University Press, OxfordGoogle Scholar
  23. Gapp K-P (1995) Object localization: selection of optimal reference objects. In: Frank AU, Kuhn W (eds) Spatial information theory. A theoretical basis for GIS. Proceedings of international conference, COSIT 95, Semmering, Austria, 21–23 Sept 1995. Springer, BerlinGoogle Scholar
  24. Gentner D, Boroditsky L (2001) Individuation, relativity, and early word learning. In: Bowerman M, Levinson SC (eds) Language, culture and cognition, vol 3., Language acquisition and conceptual developmentCambridge University Press, Cambridge, pp 215–256Google Scholar
  25. Gibson J (1979) The ecological approach to visual perception. Houghton Mifflin, BostonGoogle Scholar
  26. Goldstone RL, Barsalou LW (1998) Reuniting perception and conception. Cognition 65:231–262CrossRefGoogle Scholar
  27. Gottfried B, van de Weghe N, Billen R, de Maeyer P (eds) (2009) Behaviour monitoring and interpretation—BMI’09 studying moving objects in a three-dimensional world: Proceedings of the 3rd workshop on behaviour monitoring and interpretation (BMI’09) Ghent, Belgium, Novemb 3, 2009., AachenGoogle Scholar
  28. Gumperz JJ, Levinson SC (eds) (1996) Rethinking linguistic relativity. Cambridge University Press, CambridgeGoogle Scholar
  29. Hirschfeld LA, Gelman SA (eds) (1994) Mapping the mind: domain specificity in cognition and culture. Cambridge University Press, New YorkGoogle Scholar
  30. Jiang J, Worboys M (2009) Event-based topology for dynamic planar areal objects. Int J Geogr Inf Sci 23(1):33–60CrossRefGoogle Scholar
  31. Johnson M (1987) The body in the mind: the bodily basis of meaning, imagination, and reasoning. University of Chicago Press, ChicagoGoogle Scholar
  32. Klein F (1872) Vergleichende Betrachtungen über neuere geometrische Forschungen (“A comparative review of recent researches in geometry”). Math Ann 43:63–100CrossRefGoogle Scholar
  33. Klippel A (2012) Spatial information theory meets spatial thinking—is topology the Rosetta Stone of spatio-temporal cognition? Ann Assoc Am Geogr. doi: 10.1080/00045608.2012.702481 Google Scholar
  34. Klippel A (2009) Topologically characterized movement patterns: a cognitive assessment. Spatial Cogn Comput 9(4):233–261CrossRefGoogle Scholar
  35. Klippel A, Li R (2009) The endpoint hypothesis: a topological-cognitive assessment of geographic scale movement patterns. In: Stewart Hornsby K, Claramunt C, Denis M, Ligozat G (eds) Spatial information theory. Proceedings of 9th international conference, COSIT 2009, Aber Wrac’h, France, 21–25 Sept 2009. Springer, Berlin, pp 177–194Google Scholar
  36. Klippel A, Li R, Hardisty F, Weaver C (2010) Cognitive invariants of geographic event conceptualization: what matters and what refines. In: Fabrikant SI, Reichenbacher T, van Krefeld M, Schlieder C (eds) Proceedings of sixth international conference, GIScience 2010 Zürich, Switzerland, 14–17 Sept 2010. Springer, Berlin, pp 130–144Google Scholar
  37. Klippel A, Weaver C, Robinson AC (2011) Analyzing cognitive conceptualizations using interactive visual environments. Cartogr Geogr Inf Sci 38(1):52–68CrossRefGoogle Scholar
  38. Klippel A, Worboys M, Duckham M (2008) Identifying factors of geographic event conceptualisation. Int J Geogr Inf Sci 22(2):183–204CrossRefGoogle Scholar
  39. Klix F (1971) Information und Verhalten: Kybernetische Aspekte der organismischen Informationsverarbeitung; Einführung in naturwissenschaftliche Grundlagen der allgemeinen Psychologie. Huber, BernGoogle Scholar
  40. Knauff M, Rauh R, Renz J (1997) A cognitive assessment of topological spatial relations: results from an empirical investigation. In: Hirtle SC, Frank AU (eds) Spatial information theory: a theoretical basis for GIS. Springer, Berlin, pp 193–206CrossRefGoogle Scholar
  41. Kuhn W (2001) Ontologies in support of activities in geographic space. Int J Geogr Inf Sci 15(7):612–632CrossRefGoogle Scholar
  42. Kuhn W (2007) An image-schematic account of spatial categories. In: Winter S, Kuipers B, Duckham M, Kulik L (eds) Spatial information theory. Proceedings of 9th international conference, COSIT 2007, Melbourne, Australia, 19–23 Sept 2007. Springer, Berlin, pp 152–168Google Scholar
  43. Kurata Y (2008a) A strategy for drawing a conceptual neighborhood diagram. In: Stapleton G, Howse J, Lee J (eds) Lecture notes in computer science. Lecture notes in artificial intelligence, vol 5223. Diagrammatic representation and inference. Proceedings of 5th international conference, Diagrams 2008, Herrsching, Germany, 19–21 Sept 2008. Springer, Berlin, pp 388–390Google Scholar
  44. Kurata Y (2008b) The 9+-intersection: a universal framework for modeling topological relations. In: Cova TJ, Miller HJ, Beard K, Frank AU, Goodchild MF (eds) Geographic information science. Proceedings of 5th international conference, GIScience 2008, Park City, UT, USA, 23–26 Sept 2008. Springer, Berlin, pp 181–198Google Scholar
  45. Kurata Y, Egenhofer MJ (2009) Interpretation of behaviors from a viewpoint of topology. In: Gottfried B, Aghajan H (eds) Behaviour monitoring and interpretation. Ambient intelligence and smart environments. IOS Press, Amsterdam, pp 75–97Google Scholar
  46. Lakoff G (1987) Women, fire and dangerous things. Chicago University Press, ChicagoGoogle Scholar
  47. Lakoff G (1990) The invariance hypothesis: is abstract reason based on image schemata? Cogn Linguist 1(1):39–74CrossRefGoogle Scholar
  48. Laurence S, Margolis E (1999) Concepts and cognitive science. In: Margolis E, Laurence S (eds) Concepts. Core readings. MIT Press, Cambridge, pp 3–81Google Scholar
  49. Levenshtein V (1966) Binary codes capable of correcting deletions, insertions, and reversals. Sov Phys Doklady 10(8):707–710Google Scholar
  50. Li B, Fonseca F (2006) TDD: a comprehensive model for qualitative spatial similarity assessment. Spatial Cogn Comput 6(1):31–62CrossRefGoogle Scholar
  51. Li R, Klippel A, Yang J (2011) Geographic event conceptualization: where spatial and cognitive sciences meet. In: Carlson LA, Hölscher C, Shipley TF (eds) Proceedings of the 33rd annual conference of the cognitive science society. Cognitive Science Society, Austin, pp 3168–3173Google Scholar
  52. Lu S, Harter D (2006) The role of overlap and end state in perceiving and remembering events. In: Sun R (ed) The 28th annual conference of the cognitive science society, Vancouver, British Columbia, Canada, 26–29 July 2006. Lawrence Erlbaum, Mahwah, pp 1729–1734Google Scholar
  53. Lu S, Harter D, Graesser AC (2009) An empirical and computational investigation of perceiving and remembering event temporal relations. Cogn Sci 33:345–373CrossRefGoogle Scholar
  54. Maguire MJ, Brumberg J, Ennis M, Shipley TF (2011) Similarities in object and event segmentation: a geometric approach to event path segmentation. Spatial Cogn Comput 3:254–279CrossRefGoogle Scholar
  55. Mandler JM (1992) How to build a baby II. Conceptual primitives. Psychol Rev 99(4):587–604CrossRefGoogle Scholar
  56. Mark DM, Egenhofer MJ (1994a) Calibrating the meanings of spatial predicates from natural language: line-region relations. In: Waugh TC, Healey RG (eds) Advances in GIS research, 6th international symposium on spatial data handling, Edinburgh, Scotland, UK, pp 538–553Google Scholar
  57. Mark DM, Egenhofer MJ (1994b) Modeling spatial relations between lines and regions: Combining formal mathematical models and human subject testing. Cartogr Geogr Inf Syst 21(3):195–212Google Scholar
  58. Mark DM, Egenhofer MJ (1995a) Topology of prototypical spatial relations between lines and regions in English and Spanish. In: Proceedings, Auto Carto 12, Charlotte, North Carolina, March 1995, pp 245–254Google Scholar
  59. Medak D (1999) Lifestyles—an algebraic approach to change in identity. In: Böhlen M, Jensen C, Scholl M (eds) Lecture notes in computer science. Spatio-Temporal Database Management. Springer, Berlin, pp 19–39Google Scholar
  60. Medin DL, Wattenmaker WD, Hampson SE (1987) Family resemblance, conceptual cohesiveness, and category construction. Cogn Psychol 19(2):242–279CrossRefGoogle Scholar
  61. Montello DR (1993) Scale and multiple psychologies of space. In: Frank AU, Campari I (eds) Spatial information theory: a theoretical basis for GIS. Springer, Berlin, pp 312–321CrossRefGoogle Scholar
  62. Muller P (2002) Topological spatio-temporal reasoning and representation. Comput Intell 18(3):420–450CrossRefGoogle Scholar
  63. Peuquet DJ (1988) Representations of geographic space: toward a conceptual synthesis. Ann Assoc Am Geogr 78(3):375–394CrossRefGoogle Scholar
  64. Pothos EM, Chater N (2002) A simplicity principle in unsupervised human categorization. Cogn Sci 26(3):303–343CrossRefGoogle Scholar
  65. Pothos EM, Close J (2008) One or two dimensions in spontaneous classification: a simplicity approach. Cognition 2:581–602CrossRefGoogle Scholar
  66. Randell DA, Cui Z, Cohn AG (1992) A spatial logic based on regions and connections. In: Nebel B, Rich C, Swartout WR (eds) Proceedings of the 3rd international conference on knowledge representation and reasoning. Morgan Kaufmann, San Francisco, pp 165–176Google Scholar
  67. Renolen A (2000) Modelling the real world: conceptual modelling in spatiotemporal information system design. Trans GIS 4(1):23–42CrossRefGoogle Scholar
  68. Renz J (2002) Qualitative spatial reasoning with topological information. Springer, BerlinCrossRefGoogle Scholar
  69. Riedemann C (2005) Matching names and definitions of topological operators. In: Cohn AG, Mark DM (eds) Spatial information theory. Proceedings of international conference, COSIT 2005, Elliottville, NY, USA, 14–18 Sept 2005. Springer, Berlin, pp 165–181Google Scholar
  70. Schwering A (2007) Evaluation of a semantic similarity measure for natural language spatial relations. In: Winter S, Kuipers B, Duckham M, Kulik L (eds) Spatial information theory. Proceedings of 9th international conference, COSIT 2007, Melbourne, Australia, 19–23 Sept 2007. Springer, BerlinGoogle Scholar
  71. Schwering A (2011) Does metric really define topology, 20 May 2011 (personal communication)Google Scholar
  72. Shariff AR, Egenhofer MJ, Mark DM (1998) Natural-language spatial relations between linear and areal objects: the topology and metric of English-language terms. Int J Geogr Inf Sci 12(3):215–246Google Scholar
  73. Shaw R, McIntyre M, Mace W (1974) The role of symmetry in event perception. In: MacLeod RB, Pick HL (eds) Perception. Essays in honour of James J. Gibson. Cornell University Press, Ithaca, pp 276–310Google Scholar
  74. Sridhar M, Cohn A, Hogg D (2011) From video to RCC8: exploiting a distance based semantics to stabilise the interpretation of mereotopological relations: spatial information theory. In: Egenhofer M, Giudice N, Moratz R, Worboys M (eds) Spatial information theory. Proceedings of 10th international conference, COSIT 2011, Belfast, ME, USA, 12–16 Sept 2011. Springer, Berlin, pp 110–125Google Scholar
  75. Stock K, Cialone C (2011) Universality, Language-variability and individuality: defining linguistic building blocks for spatial relations. In: Egenhofer M, Giudice N, Moratz R, Worboys M (eds) Lecture notes in computer science. Spatial information theory. Proceedings of 10th international conference, COSIT 2011, Belfast, ME, USA, 12–16 Sept 2011. Springer, Berlin, pp 391–412Google Scholar
  76. Tversky B, Morrison JB, Betrancourt M (2002) Animation: does it facilitate? Int J Hum Comput Stud 57:247–262CrossRefGoogle Scholar
  77. Weaver C (2004) Building highly-coordinated visualizations in improvise. In: Proceedings of the IEEE symposium on information visualization 2004, Austin, TX, Oct 2004Google Scholar
  78. Worboys M, Duckham M (2006) Monitoring qualitative spatiotemporal change for geosensor networks. Int J Geogr Inf Sci 20(10):1087–1108CrossRefGoogle Scholar
  79. Xu J (2007) Formalizing natural-language spatial relations between linear objects with topological and metric properties. Int J Geogr Inf Sci 21(4):377–395CrossRefGoogle Scholar
  80. Yang J, Klippel A, Li R (in revision) Cognitive saliency of topological change under expansion and contraction. Int J Geogr Inf Sci Google Scholar
  81. Zacks JM (2004) Using movement and intentions to understand simple events. Cogn Sci 28:979–1008CrossRefGoogle Scholar
  82. Zhan FB (2002) A fuzzy set model of approximate linguistic terms in descriptions of binary topological relations between simple regions. In: Matsakis P, Sztandera LM (eds) Applying soft computing in defining spatial relations. Physica-Verlag, Heidelberg, pp 179–202CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Alexander Klippel
    • 1
    Email author
  • Rui Li
    • 1
  • Jinlong Yang
    • 1
  • Frank Hardisty
    • 1
  • Sen Xu
    • 1
  1. 1.Department of Geography, GeoVISTA CenterThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations