The Logic of Discrete Qualitative Relations

Authors Giulia Sindoni, John G. Stell

Thumbnail PDF


  • Filesize: 0.55 MB
  • 15 pages

Document Identifiers

Author Details

Giulia Sindoni
John G. Stell

Cite AsGet BibTex

Giulia Sindoni and John G. Stell. The Logic of Discrete Qualitative Relations. In 13th International Conference on Spatial Information Theory (COSIT 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 86, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


We consider a modal logic based on mathematical morphology which allows the expression of mereotopological relations between subgraphs in the setting of the discrete space. A specific form of topological closure for graphs can be expressed in the logic, as a combination of the negation and its bi-intuitionistic dual, as well as a modality, using the stable relation Q, which describes the incidence structure of the graph. By working in this context we have been able to define qualitative spatial relations between discrete regions, and to compare them with earlier works in mereotopology, both in the discrete and in the continuous space.
  • modal logic
  • qualitative spatial reasoning
  • discrete space


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. P. Blackburn, J. F. van Benthem, and F. Wolter. Handbook of modal logic, volume 3. Elsevier, 2006. Google Scholar
  2. I. Bloch. Modal logics based on mathematical morphology for qualitative spatial reasoning. Journal of Applied Non-Classical Logics, 12(3-4):399-423, 2002. Google Scholar
  3. A. G. Cohn and A. C. Varzi. Mereotopological connection. Journal of Philosophical Logic, 32:357-390, 2003. Google Scholar
  4. J. Cousty, L. Najman, F. Dias, and J. Serra. Morphological filtering on graphs. Computer Vision and Image Understanding, 117:370-385, 2013. Google Scholar
  5. M. J. Egenhofer and J. Herring. Categorizing binary topological relations between regions, lines, and points in geographic databases. Department of Surveying Engineering, , University of Maine, Orono, ME, 9(94-1):76, 1991. Google Scholar
  6. A. Galton. The mereotopology of discrete space. In C. Freksa and D. Mark, editors, COSIT'99 proceedings, volume 1661 of LNCS, pages 251-266. Springer, 1999. Google Scholar
  7. Antony Galton. Discrete mereotopology. In Mereology and the Sciences, pages 293-321. Springer, 2014. Google Scholar
  8. F. W. Lawvere. Intrinsic co-heyting boundaries and the leibniz rule in certain toposes. In Category Theory, pages 279-281. Springer, 1991. Google Scholar
  9. L. Najman and H. Talbot. Mathematical Morphology. From theory to applications. Wiley, 2010. Google Scholar
  10. D. A. Randell, Z. Cui, and A. G. Cohn. A spatial logic based on regions and connection. In B. Nebel, C. Rich, and W. Swartout, editors, Principles of Knowledge Representation and Reasoning. Proceedings of the Third International Conference (KR92), pages 165-176. Morgan Kaufmann, 1992. Google Scholar
  11. G. E. Reyes and H. Zolfaghari. Bi-Heyting algebras, toposes and modalities. Journal of Philosophical Logic, 25:25-43, 1996. Google Scholar
  12. Azriel Rosenfeld. Digital topology. American Mathematical Monthly, pages 621-630, 1979. Google Scholar
  13. P. Simons. Parts. A Study in Ontology. Clarendon Press, Oxford, 1987. Google Scholar
  14. M. B. Smyth. Topology. In Handbook of Logic in Computer Science, Vol 1, pages 641-761. Clarendon Press, Oxford, 1992. Google Scholar
  15. J. G. Stell, R. A. Schmidt, and D. Rydeheard. A bi-intuitionistic modal logic: Foundations and automation. J. Logical and Algebraic Methods in Programming, 85(4):500-519, 2016. Google Scholar
  16. J. G. Stell and M. F. Worboys. The algebraic structure of sets of regions. In S. C. Hirtle and A. U. Frank, editors, Spatial Information Theory, International Conference COSIT'97, Proceedings, volume 1329 of LNCS, pages 163-174. Springer, 1997. Google Scholar
  17. D. Vakarelov, G. Dimov, I. Düntsch, and B. Bennett. A proximity approach to some region-based theories of space. Journal of Applied Non-Classical Logics, 12:527-559, 2002. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail