Abstract
The notions of meta-ontology enhance the ability to process knowledge in information systems; in particular, ontological property classification deals with the kinds of properties in taxonomic knowledge based on a philosophical analysis. The goal of this paper is to devise a reasoning mechanism to check the ontological and logical consistency of knowledge bases, which is important for reasoning services on taxonomic knowledge. We first consider an ontological property classification that is extended to capture individual existence and time and situation dependencies. To incorporate the notion into logical reasoning, we formalize an order-sorted modal logic that involves rigidity, sortality, and three kinds of modal operators (temporal/situational/any world). The sorted expressions and modalities establish axioms with respect to properties, implying the truth of properties in different kinds of possible worlds and in varying domains in Kripke semantics. We provide a prefixed tableau calculus to test the satisfiability of such sorted modal formulas, which validates the ontological axioms of properties.
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References
Beierle, C., Hedtsück, U., Pletat, U., Schmitt, P.H., Siekmann, J.: An order-sorted logic for knowledge representation systems. Artificial Intelligence 55, 149–191 (1992)
Cerrito, S., Mayer, M.C., Praud, S.: First order linear temporal logic over finite time structures. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS, vol. 1705, pp. 62–76. Springer, Heidelberg (1999)
Cohn, A.G.: Taxonomic reasoning with many sorted logics. Artificial Intelligence Review 3, 89–128 (1989)
Fitting, M., Mendelsohn, R.L.: First-Order Modal Logic (1998)
Frisch, A.M.: The substitutional framework for sorted deduction: fundamental results on hybrid reasoning. Artificial Intelligence 49, 161–198 (1991)
Gabbay, D.M., Kurucz, A., Wolter, F., Zakharyaschev, M.: Many-Dimensional Modal Logics: Theory and Applications. Elsevier, Amsterdam (2003)
Gabelaia, D., Kontchakov, R., Kurucz, A., Wolter, F., Zakharyaschev, M.: On the computational complexity of spatio-temporal logics. In: Proc. of FLAIRS, pp. 460–464 (2003)
Garson, J.W.: Quantification in modal logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. II, pp. 249–307 (1984)
Goré, R.: Tableau methods for modal and temporal logics. In: D’Agostino, M., Gabbay, D., Hähnle, R., Posegga, J. (eds.) Handbook of Tableau Methods. Kluwer, Dordrecht (1999)
Guarino, N., Carrara, M., Giaretta, P.: An ontology of meta-level categories. In: Proc. of the 4th Int. Conf. on the Principles of Knowledge Representation and Reasoning, pp. 270–280 (1994)
Guarino, N., Welty, C.: Ontological analysis of taxonomic relationships. In: Proceedings of ER 2000: The Conference on Conceptual Modeling (2000)
Kaneiwa, K.: Order-sorted logic programming with predicate hierarchy. Artificial Intelligence 158(2), 155–188 (2004)
Kaneiwa, K., Mizoguchi, R.: Ontological knowledge base reasoning with sort-hierarchy and rigidity. In: Proc. of the 9th Int. Conf. on the Principles of Knowledge Representation and Reasoning, pp. 278–288 (2004)
Mayer, M.C., Cerrito, S.: Ground and free-variable tableaux for variants of quantified modal logics. Studia Logica 69(1), 97–131 (2001)
Schmidt-Schauss, M.: Computational Aspects of an Order-Sorted Logic with Term Declarations. Springer, Heidelberg (1989)
Schmitt, P.H., Goubault-Larrecq, J.: A tableau system for linear-TIME temporal logic. In: Brinksma, E. (ed.) TACAS 1997, vol. 1217, pp. 130–144. Springer, Heidelberg (1997)
Smith, B.: Basic concepts of formal ontology. Formal Ontology in Information Systems (1998)
Walther, C.: A mechanical solution of Schubert’s steamroller by many-sorted resolution. Artificial Intelligence 26(2), 217–224 (1985)
Welty, C., Guarino, N.: Supporting ontological analysis of taxonomic relationships. Data and Knowledge Engineering 39(1), 51–74 (2001)
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Kaneiwa, K., Mizoguchi, R. (2005). An Order-Sorted Quantified Modal Logic for Meta-ontology. In: Beckert, B. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2005. Lecture Notes in Computer Science(), vol 3702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11554554_14
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DOI: https://doi.org/10.1007/11554554_14
Publisher Name: Springer, Berlin, Heidelberg
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