Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2011 | 9 | 6 | 1354-1379
Tytuł artykułu

Logics for stable and unstable mereological relations

Treść / Zawartość
Warianty tytułu
Języki publikacji
In this paper we present logics about stable and unstable versions of several well-known relations from mereology: part-of, overlap and underlap. An intuitive semantics is given for the stable and unstable relations, describing them as dynamic counterparts of the base mereological relations. Stable relations are described as ones that always hold, while unstable relations hold sometimes. A set of first-order sentences is provided to serve as axioms for the stable and unstable relations, and representation theory is developed in similar fashion to Stone’s representation theory for distributive lattices. First-order predicate logic and modal logic are presented with semantics based on structures with stable and unstable mereological relations. Completeness theorems for these logics are proved, as well as decidability in the case of the modal logic, hereditary undecidability in the case of the first-order logic, and NP-completeness for the satisfiability problem of the quantifier-free fragment of the first-order logic.
Opis fizyczny
  • [1] Balbes R., Dwinger Ph., Distributive Lattices, University of Missouri Press, Columbia, 1974
  • [2] Balbiani Ph., Tinchev T., Vakarelov D., Modal logics for region-based theory of space, Fund. Inform., 2007, 81(1–3), 29–82
  • [3] Blackburn P., de Rijke M., Venema Y., Modal Logic, Cambridge Tracts Theoret. Comput. Sci., 53, Cambridge University Press, Cambridge, 2001
  • [4] Chagrov A., Zakharyaschev M., Modal Logic, Oxford Logic Guides, Oxford University Press, New York, 1997
  • [5] Egenhofer M.J., Franzosa R., Point-set topological spatial relations, International Journal of Geographic Information Systems, 1991, 5(2), 161–174
  • [6] Ershov Yu.L., Problems of Decidability and Constructive Models, Nauka, Moscow, 1980 (in Russian)
  • [7] Fine K., Essence and modality, Philosophical Perspectives, 1994, 8, 1–16
  • [8] Finger M., Gabbay D.M., Adding a temporal dimension to a logic system, J. Logic Lang. Inform., 1992, 1(3), 203–233
  • [9] Jonsson P., Drakengren T., A complete classification of tractability in RCC-5, J. Artificial Intelligence Res., 1997, 6, 211–221
  • [10] Kontchakov R., Kurucz A., Wolter F., Zakharyaschev M., Spatial logic + temporal logic = ?, In: Handbook of Spatial Logics, Springer, Dordrecht, 2007, 497–564
  • [11] de Laguna T., Point, line, and surface, as sets of solids, J. Philos., 1922, 19(17), 449–461
  • [12] Lutz C., Wolter F., Modal logics of topological relations, Log. Methods Comput. Sci., 2006, 2(2), #5
  • [13] Nenchev V., Vakarelov D., An axiomatization of dynamic ontology of stable and unstable mereological relations, In: 7th Panhellenic Logic Symposium, Patras, July 15–19, 2009, 137–141
  • [14] Nenov Y., Vakarelov D., Modal Llogics for mereotopological relations, In: Advances in Modal Logic, 7, Nancy, September 9–12, 2008, College Publications, London, 2008, 249–272
  • [15] Randell D.A., Cui Z., Cohn A.G., A spatial logic based on regions and connection, In: 3rd International Conference on Knowledge Representation and Reasoning, 1992, Morgan Kaufmann, 1992, 165–176
  • [16] Segerberg K., An Essay in Classical Modal Logic, Filosofiska Studier, 13, Filosofiska Föreningen och Filosofiska Institutionen vid Uppsala Universitet, Uppsala, 1971
  • [17] Simons P., Parts. A Study in Ontology, Clarendon Press, Oxford, 1987
  • [18] Vakarelov D., Logical analysis of positive and negative similarity relations in property systems, In: 1st World Conference on the Fundamentals of Artificial Intelligence, Paris, July 1–5, 1991, 491–499
  • [19] Vakarelov D., A modal logic for set relations, In: 10th International Congress of Logic, Methodology and Philosophy of Science, Florence, August 19–25, 1995, 183
  • [20] Vakarelov D., A modal approach to dynamic ontology: modal mereotopology, Logic Log. Philos., 2008, 17(1–2), 163–183
  • [21] Vakarelov D., Dynamic mereotopology: a point-free theory of changing regions. I. Stable and unstable mereotopological relations, Fund. Inform., 2010, 100, 159–180
  • [22] Whitehead A.N., Process and Reality, Cambridge University Press, Cambridge, 1929
  • [23] Wolter F., Zakharyaschev M., Spatio-temporal representation and reasoning based on RCC-8, In: 7th International Conference on Knowledge Representation and Reasoning, 2000, Morgan Kaufmann, 2000, 3–14
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.