Skip to main content
SpringerLink
Log in

An Exploratory Survey of Logic-Based Formalisms for Spatial Information

  • Chapter
Methods for Handling Imperfect Spatial Information

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 256))

Abstract

This chapter presents a tentative survey of logic-based formalisms for representing various aspects of spatial information ranging from the expression of spatial relationships between regions to the attribution of properties to definite regions. The first main part of the paper reviews the logic-based representations of mereotopologies in classical or modal logics, and in fuzzy and rough sets settings, as well as modal logic representations of geometries. The second main part is devoted to the handling of properties associated to regions. The association either relates properties to a current region of interest, or to explicitly named regions. Properties may be attached to a whole region and hold “everywhere”, or hold “somewhere”, or “elsewhere”. Properties and their localization may be also pervaded with uncertainty. This overview reveals that the many existing formalisms address different issues, and when they deal with the same issue they do it differently. However, it seems that in practice there is a need for a combination of representational capabilities, which could cover both spatial relationships and localized properties, possibly in presence of uncertainty.

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

Access this chapter

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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

  1. Aiello, M., van Benthem, J.: A modal walk through space. Journal of Applied Non Classical Logic 12(3-4), 319–364 (2002)

    Article  MATH  Google Scholar 

  2. Asher, N., Vieu, L.: Toward a Geometry of Common Sense: A Semantics and a Complete Axiomatization of Mereotopology. In: International Joint Conference on Artificial Intelligence (IJCAI), Montreal, Canada, pp. 846–852. Morgan Kaufmann Publishers, San Francisco (1995)

    Google Scholar 

  3. Balbiani, P.: The modal multilogic of geometry (1998) (manuscript )

    Google Scholar 

  4. Balbiani, P., Fariñas del Cerro, L., Tinchev, T., Vakarelov, D.: Modal logics for incidence geometries. Journal of Logic and Computation 7(1), 59–78 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Balbiani, P., Goranko, V.: Logics for parallelism, orthogonality, and affine geometries. Journal of Applied Non Classical Logic 12(3-4), 365–398 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bennett, B.: Modal logics for qualitative spatial reasoning. Bulletin of the Interest Group in Pure and Applied Logic 3(7), 1–22 (1995)

    Google Scholar 

  7. Bennett, B.: A categorical axiomatisation of region-based geometry. Fundamenta Informaticae 36(1-2), 145–158 (2001)

    Google Scholar 

  8. Bennett, B., Cohn, A.: Consistency of topological relations in the presence of convexity constraints. In: Proceedings of the ‘Hot Topics in Spatio Temporal Reasoning’ workshop, IJCAI 1999, Stockholm (1999)

    Google Scholar 

  9. Bloch, I.: Fuzzy spatial relationships for image processing and interpretation: a review. Image Vision Comput. 23(2), 89–110 (2005)

    Article  Google Scholar 

  10. Borgo, S., Guarino, N., Masolo, C.: A pointless theory of space based on strong connection and congruence. In: Carlucci Aiello, L., Doyle, J. (eds.) Principles of Knowledge Representation and Reasoning: Proc. 5th Intl. Conf (KR 1996), pp. 220–229. Morgan Kaufman, San Francisco (1996)

    Google Scholar 

  11. Bunge, M.: On null individuals. The Journal of Philosophy 63(24), 776–778 (1966)

    Article  Google Scholar 

  12. Casati, R., Varzi, A.: Holes and Other Superficialities. MIT Press, Cambridge (1994)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  14. Clarke, B.L.: A calculus of individuals based on connection. Notre Dame J. of Formal Logic 22, 204–218 (1981)

    Article  MATH  Google Scholar 

  15. Cungen, C., Yuefei, S., Zaiyue, Z.: Rough Mereology in Knowledge Representation. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639. Springer, Heidelberg (2003)

    Google Scholar 

  16. Demri, S., Orlowska, E.: Incomplete Information: Structure, Inference, Complexity. Springer, New York (2002)

    MATH  Google Scholar 

  17. Donnelly, M.: An Axiomatic Theory of Common-Sense Geometry. The University of Texas at Austin (2001)

    Google Scholar 

  18. Dubois, D., Dupin de Saint-Cyr, F., Prade, H.: A possibility-theoretic view of formal concept analysis. Fundamenta Informaticae 75, 195–213 (2007)

    MATH  MathSciNet  Google Scholar 

  19. Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of logic in Artificial Intelligence and logic programming, vol. 3, pp. 439–513. Clarendon Press, Oxford (1994)

    Google Scholar 

  20. Dubois, D., Prade, H.: Possibility Theory. Plenum Press, New York (1988)

    MATH  Google Scholar 

  21. Dugat, V., Gambarotto, P., Larvor, Y.: Qualitative geometry for shape recognition. Applied Intelligence 17(3), 253–263 (2002)

    Article  MATH  Google Scholar 

  22. Düntsch, I.: Contact relation algebras. In: Orlowska, E., Szalas, A. (eds.) Relational Methods in Algebra, Logic, and Computer Science, pp. 113–134. Physica-Verlag, Heidelberg (2001)

    Google Scholar 

  23. Düntsch, I., Orlowska, E., Wang, H.: Algebras of approximating regions. Fundamenta Informaticae 46, 71–82 (2001)

    MATH  MathSciNet  Google Scholar 

  24. Dupin de Saint-Cyr, F., Jeansoulin, R., Prade, H.: Fusing uncertain structured spatial information. In: Greco, S., Lukasiewicz, T. (eds.) SUM 2008. LNCS (LNAI), vol. 5291, pp. 174–188. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  25. Dupin de Saint-Cyr, F., Prade, H.: Logical handling of uncertain, ontology-based, spatial information. Fuzzy Sets and Systems, Advances in Intelligent Databases and Information Systems 159(12), 1515–1534 (2008)

    MATH  MathSciNet  Google Scholar 

  26. Fariñas del Cerro, L., Orlowska, E.: Dal– a logic for data analysis. Theoretical Computer Science 36, 251–264 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  27. Ganter, B., Wille, R.: Formal Concept Analysis, Mathematical Foundations. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  28. Jeansoulin, R., Mathieu, C.: Une logique des inférences spatiales. Revue internationale de géomatique 4(3-4), 369–384 (1994)

    Google Scholar 

  29. Mc Kinsey, J.C.C., Tarski, A.: The algebra of topology. Annals of Mathematics 45, 141–191 (1944)

    Article  MathSciNet  Google Scholar 

  30. Kripke, S.: Semantical analysis of Intuitionnist logic I. In: Crossley, J., Demmett, M. (eds.) Formal Systems and Recursive Functions. North Holland, Amsterdam (1963)

    Google Scholar 

  31. Kutz, O., Sturm, H., Suzuki, N., Wolter, F., Zakharyaschev, M.: Axiomatizing distance logics. Journal of Applied Non Classical Logic 12(3-4), 425–440 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  32. Kutz, O., Sturm, H., Suzuki, N.-Y., Wolter, F., Zakharyaschev, M.: Logics of metric spaces. ACM Transactions on Computational Logic (TOCL) 4(2), 260–294 (2003)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  34. Le Ber, F., Ligozat, G., Papini, O.: Raisonnements sur l’Espace et le Temps: des Modèles aux Applications. Hermes, Lavoisier eds (2007)

    Google Scholar 

  35. Lemon, O., Pratt, I.: On the incompleteness of modal logics of space. In: Advances in Modal Logic, pp. 115–132. CSLI publications, Standford (1998)

    Google Scholar 

  36. Lesniewski, S.: Sur les fondements de la mathematique. traduit du polonais par Kalinowski. Hermes, Paris (1989)

    MATH  Google Scholar 

  37. Martin, R.: Of time and null individuals. The Journal of Philosophy 62, 723–736 (1965)

    Article  Google Scholar 

  38. Marx, M., Reynolds, M.: Undecidability of compass logic. Journal of Logic and Computation 9(6), 897–914 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  39. Nicod, J.: La geometrie dans le monde sensible. In: English translation in: Geometry and Induction 1969, Presses Unitaires de France, Routledge and Kegan Paul (1962)

    Google Scholar 

  40. Orlowska, E., Pawlak, Z.: Expressive power of knowledge representation systems. International Journal of Man-Machine Studies 20, 485–500 (1984)

    Article  MATH  Google Scholar 

  41. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)

    MATH  Google Scholar 

  42. Polkowski, L.: Rough mereology: A rough set paradigm for unifying rough set theory and fuzzy set theory. Fundamenta Informaticae 54, 67–88 (2003)

    MATH  MathSciNet  Google Scholar 

  43. Polkowski, L.: Rough mereology as a link between rough set and fuzzy set theories. a survey. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds.) Transactions on Rough Sets II. LNCS, vol. 3135, pp. 253–277. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  44. Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning. International Journal of Approximate Reasoning 15, 333–365 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  45. Randell, D.A., Cui, Z., Cohn, A.: Naive topology: modeling the force pump. In: Faltings, B., Struss, P. (eds.) Recent Advances in Qualitative Reasoning. MIT Press, Cambridge (1992)

    Google Scholar 

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

    Google Scholar 

  47. Renz, J., Nebel, B.: On the complexity of qualitative spatial reasoning: A maximal tractable fragment of the region connection calculus. Artificial Intellegence 108(1-2), 69–123 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  48. Schockaert, S.: Reasoning about Fuzzy Temporal and Spatial Information from the Web. PhD dissertation. Universiteit Gent, Gent, Belgium (2008)

    Google Scholar 

  49. Schockaert, S., De Cock, M., Kerre, E.: Spatial reasoning in a fuzzy region connection calculus. Artificial Intelligence 173(2), 258–298 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  50. Segerberg, K.: A note on the logic of elsewhere. Theoria 47, 183–187 (1981)

    MathSciNet  Google Scholar 

  51. Smith, B., Varzi, A.C.: Fiat and bona fide boundaries. Philosophy and Phenomenological Research 60(2), 401–420 (2001)

    Article  Google Scholar 

  52. Sturm, H., Suzuki, N.-Y., Wolter, F., Zakharyaschev, M.: Semi-qualitative reasoning about distances: preliminary report. In: Brewka, G., Moniz Pereira, L., Ojeda-Aciego, M., de Guzmán, I.P. (eds.) JELIA 2000. LNCS (LNAI), vol. 1919, pp. 37–56. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  53. Tarski, A.: Logique, smantique, mta-mathmatique, Vol 1. Armand Colin (1972)

    Google Scholar 

  54. Tuan-Fang, F., Churn-Jung, L., Yiyu, Y.: On modal and fuzzy decision logics based on rough set theory. Fundamenta Informaticae 52, 323–344 (2002)

    MATH  MathSciNet  Google Scholar 

  55. van Benthem, J.: The Logic of Time. In: Synthese Library, vol. 156. Kluwer Academic Publishers, Dordrecht (1983) (Reidel, revisited and expanded in 1991)

    Google Scholar 

  56. Varzi, A.: Parts, wholes, and part-whole relations: The prospects of mereotopology. The Prospects of Mereotopology, Data and Knowledge Engineering 20, 259–286 (1996)

    Article  MATH  Google Scholar 

  57. Venema, Y.: Expessiveness and completeness of an interval tense logic. Notre Dame Journal Formal Logic 31(4), 529–547 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  58. Venema, Y.: Points, lines and diamonds: a two-sorted modal logic for projective planes. Journal of Logic and Computation 9(5), 601–621 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  59. Vieu, L.: Semantique des relations spatiales et inferences spatio-temporelles. PhD dissertation. Universite Paul Sabatier, Toulouse (1991)

    Google Scholar 

  60. Wolter, F., Zakharyaschev, M.: Spatial Reasoning in RCC-8 with Boolean Region Terms. In: Horn, W. (ed.) Proceedings of the 14th European Conference on Artificial Intelligence (ECAI 2000), Berlin, pp. 244–250. IOS Press, Amsterdam (2000)

    Google Scholar 

  61. Wolter, F., Zakharyaschev, M.: Spatial Reasoning in RCC-8 with Boolean Region Terms. In: Horn, W. (ed.) Proceedings of the 14th European Conference on Artificial Intelligence (ECAI 2000), Berlin, pp. 244–250. IOS Press, Amsterdam (2000)

    Google Scholar 

  62. Cristani, M.: The Complexity of Reasoning about Saptial Congruence. J. Artif. Intell. Res. (JAIR) 11, 361–390 (1999), http://dx.doi.org/10.1613/jair.641

  63. Gerevini, A., Renz, J.: Combining topological and size information for spatial reasoning. Artif. Intell. 137, 1–42 (2002)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LSIS UMR-CNRS 6168. ESIL, Université de la Méditerranée,  

    Odile Papini

  2. IRIT UMR-CNRS,  

    Florence Dupin de Saint-Cyr & Henri Prade

Authors
  1. Florence Dupin de Saint-Cyr
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Odile Papini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Henri Prade
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. IGM Université Paris Est, Champs-sur-Marne, France

    Robert Jeansoulin

  2. LSIS UMR CNRS, Marseille, France

    Odile Papini

  3. Université Paul Sabatier, Toulouse, France

    Henri Prade

  4. Ghent University, Ghent, Belgium

    Steven Schockaert

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

de Saint-Cyr, F.D., Papini, O., Prade, H. (2010). An Exploratory Survey of Logic-Based Formalisms for Spatial Information. In: Jeansoulin, R., Papini, O., Prade, H., Schockaert, S. (eds) Methods for Handling Imperfect Spatial Information. Studies in Fuzziness and Soft Computing, vol 256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14755-5_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14755-5_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14754-8

  • Online ISBN: 978-3-642-14755-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation