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Modal Logics for Region-based Theories of Space

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Abstrakty
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We dedicate thispaper to Professor Andrzej Grzegorczyk. His paper "Axiomatization of geometry without points" is one the first contributions to the region-based theory of space.
Wydawca
Rocznik
Strony
29--82
Opis fizyczny
bibliogr. 44 poz.
Twórcy
autor
autor
autor
  • Faculty of Mathematics and Informatics sofia University, 5 James Bourchier, 1164 Sofia, Bulgaria, tinko@fmi.uni-sofia.bg
Bibliografia
  • [1] BALBIANI, PH., TINCHEV, T., AND VAKARELOV, D. Dynamic Logic of Region-based Theory of Discrete Spaces. Journal of Applied Non-Classical Logic 17, 2007, 39-61.
  • [2] BALBIANI, PH., AND VAKARELOV, D. Iteration-free PDL with intersection. Fundamenta Informaticae, 45 2001, 1-22.
  • [3] BLACKBURN, P., DE RIJKE, M., VENEMA, Y.: Modal Logic. Cambridge University Press, Cambridge Tracts in Theoretical Computer Science 53 (2001).
  • [4] CLARKE, B. L. A calculus of individuals based on 'connection'. Notre Dame Journal of Formal Logic 22 (1981), 204-218.
  • [5] CHAGROV, A., ZAKHARYASCHEV, M.: Modal Logic. Oxford University Press, Oxford Logic Guides 35 (1997).
  • [6] COHN, A., AND HAZARIKA, S. Qualitative spatial representation and reasoning: An overview. Fundamenta Informaticae 46 (2001), 1-29.
  • [7] DE LAGUNA, T. Point, line and surface as sets of solids. The Journal of Philosophy 19 (1922), 449-461.
  • [8] DIMOV, G. AND VAKARELOV, D. Topological Representation of Precontact Algebras. In W. MacCaull, M. Winter and I. Düntsch Eds. RelationalMethods in Computer Science. 8th International Seminar on Relational Methods in Computer Science, 3rd InternationalWorkshop on Applications of Kleene Algebra andWorkshop of COST Action 274: TARSKI, St. Catharines, ON, Canada, February 2005, Selected Revised Papers, 1-16.
  • [9] DIMOV, G. AND VAKARELOV, D. Contact Algebras and Region-based Theory of Space. A proximity approach. I and II. Fundamenta Informaticae, Vol. 74 (2-3) (2006) 209-249, 251-282.
  • [10] DŰNTSCH, I. AND VAKARELOV, D. Region-based theory of discrette spaces: A proximity approach. In: Nadif, M., Napoli, A., SanJuan, E., and Sigayret, A. EDS, Proceedings of Fourth International Conference Journ'ees de l'informatiqueMessine, 123-129, Metz, France, 2003. Toa ppear in Discrete Applied Mathematics.
  • [11] DŰNTSCH, I. MACCAULL, W. VAKARELOV, D., AND WINTER, M. Topological Representation of Contact Lattices. In: Relational Methods in Computer Science, Springer Lecture Notes in Computer Science, No 4136, (2006), 135-147.
  • [12] DŰNTSCH, I. AND WINTER, M. A Representation theorem for Boolean Contact Algebras. Theoretical Computer Science (B), 347, 2005, 498-512.
  • [13] M. EGENHOFER, R. FRANZOSA. Point-set topological spatial relations. International Journal of Geographical Information Systems, 5 (1991), 161-174.
  • [14] ENGELKING, R. General Topology. PWN, Warszawa, 1977.
  • [15] GABBAY, D. An irreflexivity lemma with applications to axiomatizations of conditions in tense frames. In: U. Moenich (Ed.) Aspects of Philosophical Logic, Reidel-Dordrecht, 1981, 67-89.
  • [16] GABELAIA, D., KONCHAKOV, R., KURUCZ, A., AND ZAKHARYASCHEV, M. Combining spatial and temporal logics: expressiveness versus complexity. Journal of Artificial Intelligence Research, 23 (2005), 167-243.
  • [17] GALTON, A. The mereotopology of discete spaces. In: Freksa, C. andMark, D.M. EDS, Spatial Information Theory, Proceedings of the International Conference COSIT'99, Lecture Notes in Computer Science, 251-266. Springer-Verlag, 1999.
  • [18] GERLA, G. Pointless geometries. In: Handbook of Incidence Geometry, F. Buekenhout, Ed. Eslevier Science B.V., 1995, ch. 18, pp. 1015-1031.
  • [19] GORANKO, V. Axiomatizations with context rules of inference. Studia Logica, 58 (1998), 179-197.
  • [20] GRZEGORCZYK, A. Axiomatization of geometry without points. Synthese 12 (1960), 228-235.
  • [21] LEONARD, H. S, AND GOODMAN, N. The calculus of individuals and its uses. Journal of Symbolic Logic, 5, 1940, 45-55.
  • [22] LI, S. AND YING, M. Generalized Region Connection Calculus. , Artificial Intelligence, 145(1-2), 2004, 1-34
  • [23] MORMANN, T. Continuous lattices and Whiteheadian theory of space. Logic and Logical Philosophy 6 (1998), 35-54.
  • [24] NAIMPALLY, S. A., AND WARRACK, B. D. Proximity Spaces. Cambridge University Press, Cambridge, 1970.
  • [25] PAPADIMITRIOU, C.: Computational Complexity. Addison-Wesley (1994).
  • [26] PASSY, S. AND TINCHEV, T. PDL with data constants. Informattion Processing letters, 20 (1985), 35-41.
  • [27] PRATT, I. AND SHOOP, D. A complete axiom system for polygonalmereotopology of the real plane Journal of Philosophical Logic, 27(6) (1998), 621-661
  • [28] RANDELL, D. A., CUI, Z.AND COHN, A. G. 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, pp. 165-176, 1992.
  • [29] ROEPER, P. Region-based topology. Journal of Philosophical Logic 26 (1997), 251-309.
  • [30] SHCHEPIN, E, Real-valued functions and spaces close to normal. Siberian mathematical journal, 13 (1972) 820-830
  • [31] SIKORSKI, R. Boolean Algebras. Springer-Verlag, Berlin, 1964.
  • [32] SMITH, M.B. Semi-metrics, closure spaces and digital topology. Theoretical Computer Science, 151 (1995), 257-276.
  • [33] STELL, J. Boolean connection algebras: A new approach to the Region Connection Calculus. Artificial Intelligence 122 (2000), 111-136.
  • [34] THRON, W. J. Proximity structures and grills. Math. Ann. 206 (1973), 35-62.
  • [35] TARSKI, A. Les fondements de la géométrie des corps. First Polish Mathematical Congress, Lw´ow, 1927. English translation in J. H. Woodger (Ed.) (1956) in: Logic, Semantics, Metamathematics, Clarendon Press.
  • [36] VAKARELOV, D, Modal Rules for Intersection. Bulettin of Symbolic Logic, vol. 1, No 2, (1995), 264-265.
  • [37] VAKARELOV, D, Proximity Modal Logic. In: Proceedings of the 11th Amsterdam Colloquium, December 1997, 301-308.
  • [38] VAKARELOV, D. Region-Based Theory of space: Algebras of Regions, Representation Theory, and Logics. In: Dov Gabbay et al. (Eds.) Mathematical Problems from Applied Logic II. Logics for the XXIst Century, Springer, to appear in April 2007.
  • [39] VAKARELOV, D., DŰNTSCH, I. & BENNETT, B. A note on proximity spaces and connection based mereology. In C. Welty & B. Smith (Eds.), Proceedings of the 2nd International Conference on Formal Ontology in Information Systems (FOIS'01), 2001, 139-150.
  • [40] VAKARELOV, D., DIMOV, G.,DŰNTSCH, I. & BENNETT, B. A proximity approach to some region-based theory of space. Journal of Applied Non-Classical Logics, 12 (3-4) (2002), 527-559.
  • [41] VENEMA, Y. Derivation rules as antiaxioms. Journal of Symbolic Logic, 58 (1993), 1003-1034.
  • [42] WHITEHEAD, A. N. Process and reality. MacMillan, New York, 1929.
  • [43] WOLTER, F. AND M. ZAKHARYASCHEV. Spatial representation and reasoning in RCC-8 with Boolean region terms. In: Horn W. (Ed) Proceedings of the 14th European Conference on Artificial Intelligence (ECAI 2000), pages 244-248. IOS Press.
  • [44] VON WRIGHT, G. H. A new system of modal logic. In: Actes du XI Congr`es International de Philosophie, Bruxelles 1953; Amsterdam 1953, vol. 5, 59-63.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS5-0014-0027
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