Skip to main content
SpringerLink
Log in
Book cover

International Conference on Spatial Cognition

Spatial Cognition 2014: Spatial Cognition IX pp 299–311Cite as

Crossing the Boundary

Two Benchmarks for Qualitative Spatial Reasoning Bridging Relative Directions and Mereotopology

  • Conference paper

  • 1250 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8684))

Abstract

A well known problem of classical Qualitative Spatial Reasoning relying on composition tables is the strict division of different spatial aspects. For example, when dealing with relative directional relations, mereotopological relations may inherently be present without being directly expressed. We discuss how mereotopological relations may arise in constraint networks over Dipole relations and how these relations may be extracted via interdependency functions. Having made them explicit, these relations may be used to deploy reasoning methods specific to their spatial aspect. In order to further the development of Qualitative Spatial Reasoning, we present two families of benchmark problems that are cognitively easy to solve but still cannot be decided by present qualitative reasoning methods.

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

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chen, J., Cohn, A.G., Liu, D., Wang, S., Ouyang, J., Yu, Q.: A survey of qualitative spatial representations. The Knowledge Engineering Review, 1–31 (October 2013)

    Google Scholar 

  2. Cohn, A., Renz, J., Wölfl, S. (eds.): IJCAI Workshop on Benchmarks and Applications of Spatial Reasoning (2011)

    Google Scholar 

  3. van Delden, A.: Zeno: A Library for Qualitative Spatio-Temporal Reasoning (2011–2014), https://github.com/weltensegler/zeno

  4. van Delden, A., Mossakowski, T.: Mastering Left and Right - Different Approaches to a Problem that is not Straight Forward. In: KI, pp. 248–259 (2013)

    Google Scholar 

  5. Egenhofer, M., Franzosa, R.: Point-Set Topological Spatial Relations. International Journal of Geographical Information Systems 5(2), 161–174 (1991)

    Article  Google Scholar 

  6. Egenhofer, M.J.: Qualitative spatial-relation reasoning for design. In: NSF International Workshop on Studying Visual and Spatial Reasoning for Design Creativity, Aixen-Provence (2010)

    Google Scholar 

  7. Formica, A., Mazzei, M., Pourabbas, E., Rafanelli, M.: A 16-intersection matrix for the polygon-polyline topological relation for geographic pictorial query languages. In: Quirchmayr, G., Basl, J., You, I., Xu, L., Weippl, E. (eds.) CD-ARES 2012. LNCS, vol. 7465, pp. 302–316. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  8. Freksa, C.: Using Orientation Information for Qualitative Spatial Reasoning. In: Frank, A.U., Campari, I., Formentini, U. (eds.) Theories and Methods of Spatial-Temporal Reasoning in Geographic Space, vol. 639, pp. 162–178. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  9. Hoel, E.G., Samet, H.: Efficient processing of spatial queries in line segment databases. In: Günther, O., Schek, H.-J. (eds.) SSD 1991. LNCS, vol. 525, pp. 235–256. Springer, Heidelberg (1991)

    Google Scholar 

  10. Isli, A., Moratz, R.: Qualitative Spatial Representation and Reasoning: Algebraic Models for Relative Position. Tech. rep., Universität Hamburg, FB Informatik, Hamburg (1999)

    Google Scholar 

  11. Isli, A., Cabedo, L.M., Barkowsky, T., Moratz, R.: A topological calculus for cartographic entities. In: Habel, C., Brauer, W., Freksa, C., Wender, K.F. (eds.) Spatial Cognition 2000. LNCS (LNAI), vol. 1849, pp. 225–238. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  12. Levinson, S.C.: Frames of Reference and Molyneux’s Question: Crosslinguistic Evidence. In: Bloom, P., Peterson, M., Nadel, L., Garrett, M. (eds.) Language and Space, pp. 109–169. MIT Press (1996)

    Google Scholar 

  13. Ligozat, G.: Qualitative triangulation for spatial reasoning. In: Campari, I., Frank, A.U. (eds.) COSIT 1993. LNCS, vol. 716, pp. 54–68. Springer, Heidelberg (1993)

    Google Scholar 

  14. Ligozat, G.: Qualitative spatial and temporal reasoning. John Wiley & Sons (2013)

    Google Scholar 

  15. Moratz, R.: Representing Relative Direction as a Binary Relation of Oriented Points. In: Brewka, G., Coradeschi, S., Perini, A., Traverso, P. (eds.) Proc. of ECAI 2006. Frontiers in Artificial Intelligence and Applications, vol. 141, pp. 407–411. IOS Press (2006)

    Google Scholar 

  16. Moratz, R., Ragni, M.: Qualitative Spatial Reasoning about Relative Point Position. J. Vis. Lang. Comput. 19(1), 75–98 (2008)

    Article  Google Scholar 

  17. Moratz, R., Renz, J., Wolter, D.: Qualitative Spatial Reasoning about Line Segments. In: Proc. of ECAI 2000, pp. 234–238 (2000)

    Google Scholar 

  18. Moratz, R., Lücke, D., Mossakowski, T.: A condensed semantics for qualitative spatial reasoning about oriented straight line segments. Artificial Intelligence 175(16), 2099–2127 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  19. Mossakowski, T., Schröder, L., Wölfl, S.: A categorical perspective on qualitative constraint calculi. In: Qualitative Constraint Calculi: Application and Integration, Workshop Proceedings, pp. 28–39 (2006)

    Google Scholar 

  20. Musto, A., Stein, K., Eisenkolb, A., Röfer, T.: Qualitative and quantitative representations of locomotion and their application in robot navigation. In: Proc. of IJCAI 1999, pp. 1067–1072 (1999)

    Google Scholar 

  21. Nebel, B. (ed.): AAAI Spring Symposium: Benchmarking of Qualitative Spatial and Temporal Reasoning Systems (2009)

    Google Scholar 

  22. Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: Nebel, B., Rich, C., Swartout, W. (eds.) Proc. of KR 1992, pp. 165–176. Morgan Kaufmann (1992)

    Google Scholar 

  23. Renz, J., Nebel, B.: On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus. Artificial Intelligence 108(1-2), 69–123 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  24. Renz, J., Nebel, B.: Qualitative Spatial Reasoning Using Constraint Calculi. In: Aiello, M., Pratt-Hartmann, I., van Benthem, J. (eds.) Handbook of Spatial Logics, pp. 161–215. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  25. Sadahiro, Y.: Spatial relations among polygons: an exploratory analysis. Tokyo, University of Tokyo, Department of Urban Engineering Discussion Paper Series (2010)

    Google Scholar 

  26. Scivos, A., Nebel, B.: The finest of its class: The natural point-based ternary calculus formula_image for qualitative spatial reasoning. In: Freksa, C., Knauff, M., Krieg-Brückner, B., Nebel, B., Barkowsky, T. (eds.) Spatial Cognition IV. LNCS (LNAI), vol. 3343, pp. 283–303. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  27. Wölfl, S., Westphal, M.: On combinations of binary qualitative constraint calculi. In: IJCAI. pp. 967–973 (2009)

    Google Scholar 

  28. Wolter, D., Latecki, L.J.: Shape Matching for Robot Mapping. In: Zhang, C., Guesgen, H.W., Yeap, W.K. (eds.) Proc. of 8th Pacific Rim International Conference on Artificial Intelligence, pp. 693–702 (August 2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. SFB/TR 8/R4 - [LogoSpace], University of Bremen, Germany

    André van Delden

  2. National Center for Geographic Information and Analysis, School of Computing and Information Science, Department of Spatial Information Science and Engineering, University of Maine, 348 Boardman Hall, Orono, 04469, Maine, USA

    Reinhard Moratz

Authors
  1. André van Delden
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Reinhard Moratz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Universität Bremen, Enrique-Schmidt-Str. 5, 28359, Bremen, Germany

    Christian Freksa  & Thomas Barkowsky  & 

  2. Department of Computer Science, Universität Freiburg, Georges-Köhler-Allee 52, 79110, Freiburg, Germany

    Bernhard Nebel

  3. University of California, 93106, Santa Barbara, CA, USA

    Mary Hegarty

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

van Delden, A., Moratz, R. (2014). Crossing the Boundary. In: Freksa, C., Nebel, B., Hegarty, M., Barkowsky, T. (eds) Spatial Cognition IX. Spatial Cognition 2014. Lecture Notes in Computer Science(), vol 8684. Springer, Cham. https://doi.org/10.1007/978-3-319-11215-2_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-11215-2_21

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11214-5

  • Online ISBN: 978-3-319-11215-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation