Abstract
In this paper we show an extension of DLs with Generalized Quantifiers (GQs). Unlike the work of [QUA], we introduce an infinite set of GQs to the language by giving a language in which to define quantifiers. We also introduce structural or typeless quantifiers and polyadic quantifiers. Each one of these extensions greatly enhances the expressive power of the original DL beyond first order logic, while keeping a very simple syntax.
Preview
Unable to display preview. Download preview PDF.
References
Abiteboul, S., Hull, R. and Vianu, V. Foundations of Databases, Addison-Wesley, 1994.
Brachman, R. and Schmolze, J. An Overview of the KL-ONE Knowledge Representation System, Cognitive Science, vol. 9, 1985.
Badia, A., A Family of Query Languages with Generalized Quantifiers: its Definition, Properties and Expressiveness, Ph.d. thesis, Indiana University, 1997.
Barwise, J. and R. Cooper, Generalized Quantifiers and Natural Language, Linguistic and Philosophy, volume 4, 1981.
Borgida, A. On the Relative Expressiveness of Description Logics and Predicate Logics, Artificial Intelligence, vol. 82, 1996.
Calvanese, D., Lenzerini, M. and Nardi, D. A Unified Framework for Class-Based Representation Formalisms, Proceedings of the Conference on Principles of Knowledge Representation, Bonn, 1994.
Catarzi, T. and Lenzerini, M. Representing and Using Interschema Knowledge in Cooperative Information Systems, International Journal of Intelligent and Cooperative Information Systems, vol. 2, n. 4, 1993.
Dawar, A. and Hella, L. The Expressive Power of Finitely Many Generalized Quantifiers, in Proceedings of the 9th IEEE Symposium on Logic In Computer Science, 1994.
Grumbach, S. and Tollu, C., Query Languages with Counters, in Proceedings of the International Conference on Database Theory, Lecture Notes in Computer Science, number 333, Springer-Verlag, 1992.
Gyssens, M., Van Gucht, D. and Badia, A., Query Languages with Generalized Quantifiers, in Application of Logic Databases, Ramakrishnan, Ragu ed., Kluwer Academic Publishers, 1995.
Hsu, P. Y. and Parker, D. S., Improving SQL with Generalized Quantifiers, in Proceedings of the Tenth International Conference on Data Engineering, 1995.
Keenan, E. and Moss, L., Generalized Quantifiers and the Expressive Power of Natural Language, in [TM].
Lindstrom, P., First Order Predicate Logic with Generalized Quantifiers, Theoria, volume 32, 1966.
Mostowski, A., On a Generalization of Quantifiers, Fundamenta Mathematica, volume 44, 1957.
Quantz, J. how to Fit Generalized Quantifiers into Terminological Logics, Proceedings of the 10th European Conference on Artificial Intelligence, 1992.
Generalized Quantifiers in Natural Language, van Benthem, J. and ter Meulen, A., eds. Foris Publications, 1985.
Westerstahl, D., Quantifiers in Formal and Natural Languages, in Handbook of Philosophical Logic, volume IV, Gabbay, D. and Guenther, F., eds., Reidel Publishing Company, 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Badia, A. (1999). Extending description logics with generalized quantification. In: RaÅ›, Z.W., Skowron, A. (eds) Foundations of Intelligent Systems. ISMIS 1999. Lecture Notes in Computer Science, vol 1609. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0095094
Download citation
DOI: https://doi.org/10.1007/BFb0095094
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65965-5
Online ISBN: 978-3-540-48828-6
eBook Packages: Springer Book Archive