Skip to main content

Mental Models in Spatial Reasoning

  • Chapter
  • First Online:
Book cover Spatial Cognition

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1404))

Abstract

This chapter gives an overview of our ongoing experimental research in the MeMoSpace project, concerning the cognitive processes underlying human spatial reasoning. Our theoretical background is mental model theory, which conceives reasoning as a process in which mental models of the given information are constructed and inspected to solve a reasoning task. We first report some findings of our previous work and then two new experiments on spatial relational inference, which were conducted to investigate well-known effects from relational and syllogistic reasoning. (1) Continuity effect: n-term-series problems with continuous (W r 1 X, X r 2 Y, Y r 3 Z) and semi-continuous (X r 2 Y, Y r 3 Z, W r 1 X) premise order are easier than tasks with discontinuous order (Y r 3 Z, W r 1 X, X r 2 Y). (2) Figural bias: the order of terms in the premises (X r Y, Y r Z or Y r X, Z r Y) effects the order of terms in the conclusion (X r Z or Z r X). In the first experiment subjects made more errors and took more time to process the premises when in discontinuous order. In the second experiment subjects showed the general preference for the term order Z r X in the generated conclusions, modulated by a “figural bias”: subjects used X r Z more often if the premise term order was X r Y, Y r Z, whereas Z r X was used most often for the premise term order Y r X, Z r Y. Results are discussed in the framework of mental model theory with special reference to computational models of spatial reasoning.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Article  MATH  Google Scholar 

  • Berendt, B. (1996). Explaining preferred mental models in Allen inferences with a metrical model of imagery. Proceedings of the Eighteenth Annual Conference of the Cognitive Science Society. (pp. 489–494). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Byrne, R. M. J., & Johnson-Laird, P. N. (1989). Spatial reasoning. Journal of Memory and Language, 28, 564–575.

    Article  Google Scholar 

  • De Soto, L. B., London, M. & Handel, L. S. (1965). Social reasoning and spatial para-logic. Journal of Personality and Social Psychology, 2, 513–521.

    Article  Google Scholar 

  • De Vooght, G., & Vandierendonck, A. (in press). Spatial mental models in linear reasoning. Kognitionswissenschaft (Special issue “Räumliche mentale Modelle / Spatial mental models”).

    Google Scholar 

  • Ehrlich, K., & Johnson-Laird, P.N. (1982). Spatial descriptions and referential continuity. Journal of Verbal Learning and Verbal Behavior, 21, 296–306.

    Article  Google Scholar 

  • Evans, J. St. B. T., Newstead, S. E., & Byrne, R. M. J. (1993). Human reasoning. The psychology of deduction. Hove (UK): Lawrence Erlbaum Associates.

    Google Scholar 

  • Freksa, C. (1991). Qualitative spatial reasoning. In D. M. Mark & A. U. Frank (Eds.), Cognitive and linguistic aspects of geographic space (pp. 361–372). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Gapp, K.-P. (1997). Objektlokalisation [Object Localisation]. Wiesbaden: Deutscher Universitäts-Verlag.

    Google Scholar 

  • Hunter, I. M. L. (1957). The solving of three-term series problems. British Journal of Psychology, 48, 286–298.

    Google Scholar 

  • Johnson-Laird, P. N. (1972). The three-term series problem. Cognition, 1, 58–82.

    Article  Google Scholar 

  • Johnson-Laird, P. N. (1983). Mental models. Towards a cognitive science of language, inference, and consciousness. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Johnson-Laird, P. N., & Bara, B. G. (1984). Syllogistic reasoning. Cognition, 16, 1–62.

    Article  Google Scholar 

  • Johnson-Laird, P. N., & Byrne, R.M.J. (1991). Deduction. Hove: Lawrence Erlbaum Associates.

    Google Scholar 

  • Johnson-Laird, P. N., & Steedman, M. (1978). The psychology of syllogisms. Cognitive Psychology, 10, 64–99.

    Article  Google Scholar 

  • Knauff, M. (1997). Räumliches Wissen und Gedächtnis [Spatial knowledge and memory]. Wiesbaden: Deutscher Universitäts-Verlag

    Google Scholar 

  • Knauff, M., Rauh, R., & Renz, J. (1997). A cognitive assessment of topological spatial relations: Results from an empirical investigation. In S. C. Hirtle & A. U. Frank (Eds.), Spatial information theory. A theoretical basis for GIS. Proceedings of COSIT’ 97 (pp.193–206). New York: Springer.

    Chapter  Google Scholar 

  • Knauff, M., Rauh, R., & Schlieder, C. (1995). Preferred mental models in qualitative spatial reasoning: A cognitive assessment of Allen’s calculus. In Proceedings of the Seventeenth Annual Conference of the Cognitive Science Society (pp. 200–205). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Knauff, M. Rauh, R., Schlieder, C., & Strube, G. (1997). Analogizität und Perspektive in räumlichen mentalen Modellen [Analog representation and perspective in spatial mental models]. In C. Umbach, M. Grabski & R. Hörnig (Hrsg.). Perspektive in Sprache und Raum (pp. 35–60). Wiesbaden: Deutscher Universitäts-Verlag.

    Google Scholar 

  • Knauff, M., Rauh, R., Schlieder, C., & Strube, G. (1998). Continuity effect and figural bias in spatial relational inference. Submitted to the Twentieth Annual Conference of the Cognitive Science Society, Madison-Wisconsin.

    Google Scholar 

  • Kosslyn, S. M. (1994). Image and brain. Cambridge, MA: MIT Press.

    Google Scholar 

  • Ligozat, G. (1990). Weak representations of interval algebras. Proceedings of the Eighth. National Conference on Artificial Intelligence (Vol. 2, pp. 715–720). Menlo Park, CA: AAAI Press / MIT Press.

    Google Scholar 

  • Logie, R. H. (1995). Visuo-spatial working memory. Hove: Lawrence Erlbaum.

    Google Scholar 

  • Maybery, M.T., Bain, J.D., & Halford, G. S. (1986). Information-processing demands of transitive inference. Journal of Experimental Psychology: Learning, Memory, and Cognition, 12, 600–613.

    Article  Google Scholar 

  • Nebel, B., & Bürckert, H.J. (1995). Reasoning about temporal relations: A maximal tractable subclass of Allen’s interval algebra. Communication of the ACM, 42, 43–66.

    Google Scholar 

  • Potts, G. R., & Scholz, K.W. (1975). The internal representation of a three-term series problem. Journal of Verbal Learning and Verbal Behavior, 14, 439–452.

    Article  Google Scholar 

  • Rauh, R., & Schlieder, C. (1997). Symmetries of model construction in spatial relational inference. In Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society (pp. 638–643). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Rauh, R., Schlieder, C., & Knauff, M. (1997). Präferierte mentale Modelle beim räumlich-relationalen Schließen: Empirie und kognitive Modellierung [Preferred mental models in spatial relational inference: Empirical results and cognitive modeling]. Kognitionswissenschaft, 6, 21–34.

    Article  Google Scholar 

  • Rips, L. J. (1994). The psychology of proof. Cambridge, MA: MIT Press.

    MATH  Google Scholar 

  • Schlieder, C. (1995). The construction of preferred mental models in reasoning with the interval relations (Tech. Rep. 5/95). Freiburg: Institut für Informatik und Gesellschaft der Albert-Ludwigs-Universität Freiburg (appears also in: C. Habel & al. (Eds.), Mental models in discourse comprehension and reasoning).

    Google Scholar 

  • Trabasso, T., Riley, C. A., & Wilson, E. G. (1975). The representation of linear orders and spatial strategies in reasoning. A developmenal study. In R. J. Falmagne (Ed.), Reasoning: Representation and Processes. New York: Wiley.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Knauff, M., Rauh, R., Schlieder, C., Strube, G. (1998). Mental Models in Spatial Reasoning. In: Freksa, C., Habel, C., Wender, K.F. (eds) Spatial Cognition. Lecture Notes in Computer Science(), vol 1404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69342-4_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-69342-4_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64603-7

  • Online ISBN: 978-3-540-69342-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics