Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Frontiers of Combining Systems

FroCoS 2017: Frontiers of Combining Systems pp 281–297Cite as

Finitariness of Elementary Unification in Boolean Region Connection Calculus

  • Conference paper
  • First Online:

  • 432 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10483))

Abstract

Boolean Region Connection Calculus is a formalism for reasoning about the topological relations between regions. In this paper, we provide computability results about unifiability in Boolean Region Connection Calculus and prove that elementary unification is finitary.

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   54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
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

References

  1. Baader, F., Borgwardt, S., Morawska, B.: Extending unification in \(\cal{EL}\) towards general TBoxes. In: Principles of Knowledge Representation and Reasoning, pp. 568–572. AAAI Press (2012)

    Google Scholar 

  2. Baader, F., Ghilardi, S.: Unification in modal and description logics. Logic J. IGPL 19, 705–730 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Balbiani, P., Tinchev, T.: Boolean logics with relations. J. Logic Algebr. Program. 79, 707–721 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Balbiani, P., Tinchev, T.: Definability and canonicity for Boolean logic with a binary relation. Fundamenta Informaticæ 129, 301–327 (2014)

    MathSciNet  MATH  Google Scholar 

  5. Balbiani, P., Tinchev, T., Vakarelov, D.: Modal logics for region-based theories of space. Fundamenta Informaticæ 81, 29–82 (2007)

    MathSciNet  MATH  Google Scholar 

  6. Cohn, A., Renz, J.: Qualitative spatial representation and reasoning. In: Handbook of Knowledge Representation, pp. 551–596. Elsevier (2008)

    Google Scholar 

  7. Dimov, G., Vakarelov, D.: Contact algebras and region-based theory of space: a proximity approach – I. Fundamenta Informaticæ 74, 209–249 (2006)

    MathSciNet  MATH  Google Scholar 

  8. Dimov, G., Vakarelov, D.: Contact algebras and region-based theory of space: proximity approach – II. Fundamenta Informaticæ 74, 251–282 (2006)

    MathSciNet  MATH  Google Scholar 

  9. Düntsch, I., Winter, M.: A representation theorem for Boolean contact algebras. Theor. Comput. Sci. 347, 498–512 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dzik, W.: Unification Types in Logic. Wydawnicto Uniwersytetu Slaskiego (2007)

    Google Scholar 

  11. Galton, A.: Qualitative Spatial Change. Oxford University Press, Oxford (2000)

    MATH  Google Scholar 

  12. Gencer, Ç., de Jongh, D.: Unifiability in extensions of \(K4\). Logic J. IGPL 17, 159–172 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ghilardi, S.: Best solving modal equations. Ann. Pure Appl. Logic 102, 183–198 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kontchakov, R., Pratt-Hartmann, I., Wolter, F., Zakharyaschev, M.: Spatial logics with connectedness predicates. Logical Methods Comput. Sci. 6, 1–43 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kontchakov, R., Pratt-Hartmann, I., Zakharyaschev, M.: Interpreting topological logics over Euclidean spaces. In: Proceedings of the Twelfth International Conference on the Principles of Knowledge Representation and Reasoning, pp. 534–544. AAAI Press (2010)

    Google Scholar 

  16. Kontchakov, R., Nenov, Y., Pratt-Hartmann, I., Zakharyaschev, M.: Topological logics with connectedness over Euclidean spaces. ACM Trans. Comput. Logic 14, 1–13 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Li, S., Ying, M.: Region connection calculus: its model and composition table. Artif. Intell. 145, 121–146 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  18. Martin, U., Nipkow, T.: Boolean unification – the story so far. J. Symbol. Comput. 7, 275–293 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  19. Randell, D., Cui, Z., Cohn, A.: A spatial logic based on regions and connection. In: Proceedings of the Third International Conference on Principles of Knowledge Representation and Reasoning, pp. 165–176. Morgan Kaufman (1992)

    Google Scholar 

  20. Renz, J.: Qualitative Spatial Reasoning with Topological Information. Lecture Notes in Artificial Intelligence, vol. 2293. Springer, Heidelberg (2002). doi:10.1007/3-540-70736-0

    MATH  Google Scholar 

  21. Renz, J., Nebel, B.: On the complexity of qualitative spatial reasoning: a maximal tractable fragment of the region connection calculus. Artif. Intell. 108, 69–123 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  22. Rybakov, V.: Admissibility of Logical Inference Rules. Elsevier, Amsterdam (1997)

    MATH  Google Scholar 

  23. Vakarelov, D.: Region-based theory of space: algebras of regions, representation theory, and logics. In: Gabbay, D.M., Zakharyaschev, M., Goncharov, S.S. (eds.) Mathematical Problems from Applied Logic II. International Mathematical Series, vol. 5. Springer, New York (2007). doi:10.1007/978-0-387-69245-6_6

    Chapter  Google Scholar 

  24. Wolter, F., Zakharyaschev, M.: Spatio-temporal representation and reasoning based on \(RCC\)-\(8\). In: Proceedings of the Seventh International Conference on Principles of Knowledge Representation and Reasoning, pp. 3–14. Morgan Kaufmann (2000)

    Google Scholar 

Download references

Acknowledgements

We make a point of thanking Joseph Boudou, Yannick Chevalier and Tinko Tinchev who contributed to the development of the work we present today.

Author information

Authors and Affiliations

  1. Institut de recherche en informatique de Toulouse, CNRS—Toulouse University, Toulouse, France

    Philippe Balbiani

  2. Faculty of Engineering and Natural Sciences, Sabancı University, Istanbul, Turkey

    Çiğdem Gencer

  3. Faculty of Arts and Sciences, Aydın University, Istanbul, Turkey

    Çiğdem Gencer

Authors
  1. Philippe Balbiani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Çiğdem Gencer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Philippe Balbiani .

Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Clare Dixon

  2. University of Sao Paulo, Sao Paulo, Brazil

    Marcelo Finger

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Balbiani, P., Gencer, Ç. (2017). Finitariness of Elementary Unification in Boolean Region Connection Calculus. In: Dixon, C., Finger, M. (eds) Frontiers of Combining Systems. FroCoS 2017. Lecture Notes in Computer Science(), vol 10483. Springer, Cham. https://doi.org/10.1007/978-3-319-66167-4_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66167-4_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66166-7

  • Online ISBN: 978-3-319-66167-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation