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Extended distributive contact lattices and extended contact algebras

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Konferencja
Federated Conference on Computer Science and Information Systems (15 ; 06-09.09.2020 ; Sofia, Bulgaria)
Języki publikacji
EN
Abstrakty
EN
The notion of contact algebra is one of the main tools in mereotopology. This paper considers a generalisation of contact algebra (called extended distributive contact lattice) and the so called extended contact algebras which extend the language of contact algebras by the predicates covering and internal connectedness.
Rocznik
Tom
Strony
69--75
Opis fizyczny
Bibliogr. 30 poz., wz., rys.
Twórcy
  • Bulgarian Academy of Sciences, Institute of Mathematics and Informatics in Sofia, 1113, Sofia, Bulgaria, Acad. Georgi Bonchev Str., Block 8
Bibliografia
  • 1. M. Aiello, I. Pratt-Hartmann and J. van Benthem (Eds.), Handbook of spatial logics. Springer, 2007.
  • 2. J. F. Allen, “Maintaining knowledge about temporal intervals,” Communications of the ACM, vol. 26, (11), 1983, pp. 832–843.
  • 3. P. Balbiani (Ed.), Special Issue on Spatial Reasoning, J. Appl. Non-Classical Logics, vol. 12, (3-4), 2002.
  • 4. P. Balbiani and T. Ivanova, “Relational representation theorems for extended contact algebras,” Stud Logica, to appear, also available online with different title: https://arxiv.org/abs/1901.10367
  • 5. P. Balbiani, T. Tinchev and D. Vakarelov, “Modal logics for regionbased theory of space,” Fundamenta Informaticae, Special Issue: Topics in Logic, Philosophy and Foundation of Mathematics and Computer Science in Recognition of Professor Andrzej Grzegorczyk, vol. 81, (1-3), 2007, pp. 29–82.
  • 6. B. Bennett, “Determining consistency of topological relations,” Constraints, vol. 3, 1998, pp. 213–225.
  • 7. B. Bennett and I. Düntsch, “Axioms, algebras and topology,” in Handbook of Spatial Logics, M. Aiello, I. Pratt, and J. van Benthem (Eds.), Springer, 2007, pp. 99–160.
  • 8. A. Cohn and S. Hazarika, “Qualitative spatial representation and reasoning: An overview,” Fuandamenta informaticae, vol. 46, 2001, pp. 1–20.
  • 9. A. Cohn and J. Renz, “Qualitative spatial representation and reasoning,” in F. van Hermelen, V. Lifschitz and B. Porter (Eds.) Handbook of Knowledge Representation, Elsevier, 2008, pp. 551–596.
  • 10. G. Dimov and D. Vakarelov, “Contact algebras and region–based theory of space: A proximity approach I,” Fundamenta Informaticae, vol. 74, (2-3), 2006, pp. 209–249.
  • 11. I. Düntsch (Ed.), Special issue on Qualitative Spatial Reasoning, Fundam. Inform., vol. 46, 2001.
  • 12. I. Düntsch, W. MacCaull, D. Vakarelov and M. Winter, “Topological representation of contact lattices,” Lecture Notes in Computer Science, vol. 4136, 2006, pp. 135–147.
  • 13. I. Düntsch, W. MacCaull, D. Vakarelov and M. Winter, “Distributive contact lattices: Topological representation,” Journal of logic and Algebraic Programming, vol. 76, 2008, pp. 18–34.
  • 14. I. Düntsch and D. Vakarelov, “Region-based theory of discrete spaces: A proximity approach,” in M. Nadif, A. Napoli, E. SanJuan and A. Sigayret (Eds.) Proceedings of Fourth International Conference Journées de l’informatique Messine, Metz, France, 2003, pp. 123–129, Journal version in Annals of Mathematics and Artificial Intelligence, vol. 49, (1-4), 2007, pp. 5–14.
  • 15. I. Düntsch and M. Winter, “A representation theorem for Boolean contact algebras,” Theoretical Computer Science (B), vol. 347, 2005, pp. 498–512.
  • 16. T. Hahmann and M. Gruninger, “Region-based theories of space: Mereotopology and beyond,” S. Hazarika (ed.): Qualitative Spatio-Temporal Representation and Reasoning: Trends and Future Directions, 2012, pp. 1–62, IGI Publishing.
  • 17. Qualitative spatio-temporal representation and reasoning: Trends and future directions. S. M. Hazarika (Ed.), IGI Global, 1st ed., 2012.
  • 18. T. Ivanova, “Extended contact algebras and internal connectedness,” Stud Logica, vol. 108, 2020, pp. 239–254.
  • 19. T. Ivanova, “Logics for extended distributive contact lattices,” Journal of Applied Non-Classical Logics, vol. 28(1), 2018, pp. 140–162.
  • 20. T. Ivanova and D. Vakarelov, “Distributive mereotopology: extended distributive contact lattices,” Annals of Mathematics and Artificial Intelligence, vol. 77(1), 2016, pp. 3–41.
  • 21. T. de Laguna, “Point, line and surface as sets of solids,” J. Philos, vol. 19, 1922, pp. 449–461.
  • 22. I. Pratt-Hartmann, “First-order region-based theories of space,” in Logic of Space, M. Aiello, I. Pratt-Hartmann and J. van Benthem (Eds.), Springer, 2007.
  • 23. D. A. Randell, Z. Cui, and A. G. Cohn., “A spatial logic based on regions and connection,” in B. Nebel, W. Swartout, C. Rich (Eds.) Proceedings of the 3rd International Conference Knowledge Representation and Reasoning, Morgan Kaufmann, Los Allos, CA, 1992, pp. 165–176.
  • 24. J. Renz and B. Nebel, “On the complexity of qualitative spatial reasoning: a maximal tractable fragment of the region connection calculus,” Artificial Intelligence, vol. 108, 1999, pp. 69–123.
  • 25. J. Stell, “Boolean connection algebras: A new approach to the Region Connection Calculus,” Artif. Intell., vol. 122, 2000, pp. 111–136.
  • 26. D. Vakarelov, “Region-based theory of space: Algebras of regions, representation theory and logics,” in D. Gabbay, S. Goncharov and M. Zakharyaschev (Eds.) Mathematical Problems from Applied Logic II. Logics for the XXIst Century, Springer, 2007, pp. 267–348.
  • 27. D. Vakarelov, G. Dimov, I. Düntsch, and B. Bennett, “A proximity approach to some region based theory of space,” Journal of applied non-classical logics, vol. 12, (3-4), 2002, pp. 527–559.
  • 28. D. Vakarelov, I. Düntsch and B. Bennett, “A note on proximity spaces and connection based mereology,” in C. Welty and B. Smith (Eds.) Proceedings of the 2nd International Conference on Formal Ontology in Information Systems (FOIS’01), ACM, 2001, pp. 139–150.
  • 29. H. de Vries, “Compact spaces and compactifications,” Van Gorcum, 1962.
  • 30. A. N. Whitehead, “Process and Reality,” New York, MacMillan, 1929.
Uwagi
1. This paper is supported by contract DN02/15/19.12.2016 "Space, Time and Modality: Relational, Algebraic and Topological Models" with Bulgarian NSF.
2. Track 1: Artificial Intelligence
3. Technical Session: 15th International Symposium Advances in Artificial Intelligence and Applications
4. Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-ca3b317b-d3e3-4d2b-a923-86516167b108
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