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Casl Specifications of Qualitative Calculi

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Spatial Information Theory (COSIT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 3693))

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Abstract

In AI a large number of calculi for efficient reasoning about spatial and temporal entities have been developed. The most prominent temporal calculi are the point algebra of linear time and Allen’s interval calculus. Examples of spatial calculi include mereotopological calculi, Frank’s cardinal direction calculus, Freksa’s double cross calculus, Egenhofer and Franzosa’s intersection calculi, and Randell, Cui, and Cohn’s region connection calculi.

These calculi are designed for modeling specific aspects of space or time, respectively, to the effect that the class of intended models may vary widely with the calculus at hand. But from a formal point of view these calculi are often closely related to each other. For example, the spatial region connection calculus RCC5 may be considered a coarsening of Allen’s (temporal) interval calculus. And vice versa, intervals can be used to represent spatial objects that feature an internal direction.

The central question of this paper is how these calculi as well as their mutual dependencies can be axiomatized by algebraic specifications. This question will be investigated within the framework of the Common Algebraic Specification Language (Casl), a specification language developed by the Common Framework Initiative for algebraic specification and development CoFI. We explain scope and expressiveness of Casl by discussing the specifications of some of the calculi mentioned before.

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References

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

    Article  MATH  Google Scholar 

  2. Bennett, B.: Logical Representations for Automated Reasoning about Spatial Relationships. PhD thesis, School of Computer Studies, The University of Leeds (1997)

    Google Scholar 

  3. Bennett, B., Isli, A., Cohn, A.G.: When does a composition table provide a complete and tractable proof procedure for a relational constraint language? In: Proceedings of the IJCAI 1997 Workshop on Spatial and Temporal Reasoning, Nagoya, Japan (1997)

    Google Scholar 

  4. Bidoit, M., Mosses, P.D.: CASL User Manual. LNCS. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  5. Broxvall, M.: The point algebra for branching time revisited. In: Baader, F., Brewka, G., Eiter, T. (eds.) KI 2001. LNCS (LNAI), vol. 2174, pp. 106–121. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Broxvall, M., Jonsson, P.: Towards a complete classification of tractability in point algebras for nonlinear time. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 129–143. Springer, Heidelberg (1999)

    Google Scholar 

  7. Cohn, A.G., Bennett, B., Gooday, J.M., Gotts, N.: RCC: A calculus for region based qualitative spatial reasoning. GeoInformatica 1, 275–316 (1997)

    Article  Google Scholar 

  8. Düntsch, I., Wang, H., McCloskey, S.: Relation algebras in qualitative spatial reasoning. Fundamenta Informaticae 39(3), 229–249 (1999)

    MathSciNet  Google Scholar 

  9. Egenhofer, M.J.: Reasoning about binary topological relations. In: Günther, O., Schek, H.-J. (eds.) SSD 1991. LNCS, vol. 525, pp. 143–160. Springer, Heidelberg (1991)

    Google Scholar 

  10. Egenhofer, M.J., Franzosa, R.D.: Point set topological relations. International Journal of Geographical Information Systems 5, 161–174 (1991)

    Article  Google Scholar 

  11. Frank, A.U.: Qualitative spatial reasoning with cardinal directions. In: Kaindl, H. (ed.) Proceedings of the Seventh Austrian Conference on Artificial Intelligence. Informatik-Fachberichte 287, pp. 157–167. Springer, Heidelberg (1991)

    Google Scholar 

  12. Frank, A.U.: One step up the abstraction ladder: Combining algebras - from functional pieces to a whole. In: Freksa, C., Mark, D.M. (eds.) COSIT 1999. LNCS, vol. 1661, pp. 95–107. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  13. Freksa, C.: Using orientation information for qualitative spatial reasoning. In: Frank, A.U., Formentini, U., Campari, I. (eds.) GIS 1992. LNCS, vol. 639, pp. 162–178. Springer, Heidelberg (1992)

    Google Scholar 

  14. Gerevini, A., Renz, J.: Combining topological and qualitative size constraints for spatial reasoning. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 220–234. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  15. Hayes, P.J.: The naive physics manifesto. In: Michie, D. (ed.) Expert Systems in the Micro-Electronic Age, Edinburgh University Press (1978)

    Google Scholar 

  16. 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 

  17. Ligozat, G., Renz, J.: What is a qualitative calculus? A general framework. In: Zhang, C., Guesgen, H.W., Yeap, W.-K. (eds.) PRICAI 2004. LNCS (LNAI), vol. 3157, pp. 53–64. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  18. Mossakowski, T.: Heterogeneous specification and the heterogeneous tool set. Habilitation thesis, University of Bremen (2005)

    Google Scholar 

  19. Mosses, P.D. (ed.): CASL Reference Manual. LNCS, vol. 2960. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  20. Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)

    Book  MATH  Google Scholar 

  21. Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: Nebel, B., Swartout, W., Rich, C. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the 3rd International Conference (KR 1992), pp. 165–176. Morgan Kaufmann, San Francisco (1992)

    Google Scholar 

  22. Schröder, L., Mossakowski, T.: HASCASL: Towards integrated specification and development of functional programs. In: Kirchner, H., Ringeissen, C. (eds.) AMAST 2002. LNCS, vol. 2422, pp. 99–116. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  23. Stell, J.G.: Boolean connection algebras: A new approach to the Region-Connection Calculus. Artificial Intelligence 122(1-2), 111–136 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  24. Vilain, M.B.: A system for reasoning about time. In: Waltz, D.L. (ed.) Proceedings of the National Conference on Artificial Intelligence, Pittsburgh, PA, August 18-20, pp. 197–201. AAAI Press, Menlo Park (1982)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Freiburg, Georges-Köhler-Allee, 79110, Freiburg, Germany

    Stefan Wölfl

  2. Department of Computer Science, University of Bremen, P.O. Box 330440, 28334, Bremen, Germany

    Till Mossakowski

Authors
  1. Stefan Wölfl
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  2. Till Mossakowski
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Editor information

Editors and Affiliations

  1. School of Computing, University of Leeds, LS2 9JT, Leeds, United Kingdom

    Anthony G. Cohn

  2. Department of Geography, State University of New York at Buffalo, 105 Wilkeson Quad, 14261, Buffalo, NY, USA

    David M. Mark

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© 2005 Springer-Verlag Berlin Heidelberg

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Wölfl, S., Mossakowski, T. (2005). Casl Specifications of Qualitative Calculi. In: Cohn, A.G., Mark, D.M. (eds) Spatial Information Theory. COSIT 2005. Lecture Notes in Computer Science, vol 3693. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556114_13

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  • DOI: https://doi.org/10.1007/11556114_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28964-7

  • Online ISBN: 978-3-540-32020-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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