Abstract
Pratt and Third’s syllogistic fragments of English can be used to capture, in addition to syllogistic reasoning, many other kinds of common sense reasoning, and, in particular (i) knowledge base consistency and (ii) knowledge base query answering, modulo their FO semantic representations. We show how difficult, in terms of semantic (computational) complexity and data complexity (i.e., computational complexity w.r.t. the number of instances declared in a knowledge base), such reasoning problems are. In doing so, we pinpoint also those fragments for which the reasoning problems are tractable (in PTime) or intractable (NP-hard or coNP-hard).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)
Bernardi, R., Bonin, F., Carbotta, D., Calvanese, D., Thorne, C.: English querying over ontologies: E-QuOnto. In: Proc. of the 10th Congress of the Italian Association for Artificial Intelligence AI*IA 2007 (2007)
Bernardi, R., Calvanese, D., Thorne, C.: Expressing DL-Lite ontologies with controlled English. In: Proc. of the 20th Int. Workshop on Description Logics, DL 2007 (2007)
Calvanese, D., de Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Efficiently managing data intensive ontologies. In: Proc. of the 2nd Italian Semantic Web Workshop: Semantic Web Applications and Perspectives, SWAP 2005 (2005)
Fermüller, C.G., Leitsch, A., Hustadt, U., Tammet, T.: Resolution decision procedures. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 2, ch. 2, 1791–1849. Elsevier - The MIT Press (2001)
Joyner, W.H.: Resolution strategies as decision procedures. Journal of the ACM 23(3), 398–417 (1976)
Jurafsky, D., Martin, J.: Speech and Language Processing. Prentice-Hall, Englewood Cliffs (2000)
Montague, R.: Universal grammar. Theoria 36(3), 373–398 (1970)
Pratt, I.: Data complexity of the two-variable fragment with counting quantifiers. Information and Computation 207(8), 867–888 (2008)
Pratt, I., Third, A.: More fragments of language. Notre Dame Journal of Formal Logic 47(2), 151–177 (2006)
Pratt-Hartmann, I.: Computational complexity of controlled natural languages. In: Proc. of the Workshop in Controlled Languages CNL 2009 (2009)
Schaerf, A.: On the complexity of the instance checking problem in concept languages with existential quantification. Journal of Intelligent Information Systems 2(3), 265–278 (1993)
Slavkovik, M.: Deep analysis for an interactive question answering system. Master’s thesis, Free University of Bozen-Bolzano (2007)
Staab, S., Studer, R. (eds.): Handbook on Ontologies. Int. Handbooks on Information Systems. Springer, Heidelberg (2004)
Szymanik, J.: The computational complexity of quantified reciprocals. In: Proc. of the 2007 Tbilisi Colloquium, TbiLLC 2007 (2007)
Thorne, C., Calvanese, D.: Tree shaped aggregate queries over ontologies. In: Proc. of the 8th Int. Conf. on Flexible Query Answering Systems FQAS 2009 (2009)
Vardi, M.: The complexity of relational query languages. In: Proc. of the 14th Annual ACM Symposium on Theory of Computing, STOC 1982 (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Thorne, C., Calvanese, D. (2010). The Data Complexity of the Syllogistic Fragments of English. In: Aloni, M., Bastiaanse, H., de Jager, T., Schulz, K. (eds) Logic, Language and Meaning. Lecture Notes in Computer Science(), vol 6042. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14287-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-14287-1_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14286-4
Online ISBN: 978-3-642-14287-1
eBook Packages: Computer ScienceComputer Science (R0)