Abstract
We study the data complexity of instance checking and conjunctive query answering in the \(\mathcal{EL}\) family of description logics, with a particular emphasis on the boundary of tractability. We identify a large number of intractable extensions of \(\mathcal{EL}\), but also show that in \(\mathcal{ELI}^f\), the extension of \(\mathcal{EL}\) with inverse roles and global functionality, conjunctive query answering is tractable regarding data complexity. In contrast, already instance checking in \(\mathcal{EL}\) extended with only inverse roles or global functionality is ExpTime-complete regarding combined complexity.
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References
Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: DL-Lite in the light of first-order logic. In: AAAI 2007. Proc. of the 22nd Conf. on AI, AAAI Press, Stanford, California, USA (2007)
Baader, F., Brandt, S., Lutz, C.: Pushing the \(\mathcal{EL}\) envelope. In: IJCAI 2005. Proc. of the 19th Int. Joint Conf. on AI, pp. 364–369. Morgan Kaufmann, San Francisco (2005)
Baader, F., Brandt, S., Lutz, C.: Pushing the \(\mathcal{EL}\) envelope. (submitted to a Journal, 2007)
Baader, F., Lutz, C., Suntisrivaraporn, B.: Is tractable reasoning in extensions of the description logic \(\mathcal{EL}\) useful in practice? In: M4M 2005. Proc. of the 4th Int. WS on Methods for Modalities (2005)
Baader, F., McGuiness, D.L., Nardi, D., Patel-Schneider, P.: The Description Logic Handbook: Theory, implementation and applications. Cambridge University Press, Cambridge (2003)
Brandt, S.: Polynomial time reasoning in a description logic with existential restrictions, GCI axioms, and—what else? In: ECAI 2004. Proc. of the 16th European Conf. on AI, pp. 298–302. IOS Press, Amsterdam (2004)
Calvanese, D., Giacomo, G.D., Lembo, D., Lenzerini, M., Rosati, R.: DL-lite: Tractable description logics for ontologies. In: AAAI 2005. Proc. of the 20th National Conf. on AI, pp. 602–607. AAAI Press, Stanford, California, USA (2005)
Calvanese, D., Giacomo, G.D., Lembo, D., Lenzerini, M., Rosati, R.: Data complexity of query answering in description logics. In: KR 2006. Proc. of the 10th Int. Conf. on KR, AAAI Press, Stanford, California, USA (2006)
Calvanese, D., Giacomo, G.D., Lenzerini, M., Rosati, R., Vetere, G.: DL-lite: Practical reasoning for rich dls. In: DL 2004. CEUR Workshop Proceedings. CEUR-WS.org, vol. 104 (2004)
Glimm, B., Horrocks, I., Lutz, C., Sattler, U.: Conjunctive Query Answering for the Description Logic \(\mathcal{SHIQ}\). In: IJCAI 2007. Proc. of the 20th Int. Joint Conf. on AI, AAAI Press, Stanford, California, USA (2007)
Giacomo, G.D., Lenzerini, M.: Boosting the correspondence between description logics and propositional dynamic logics. In: AAAI 1994. Proc. of the 12th National Conf. on AI, vol. 1, pp. 205–212. AAAI Press, Stanford, California, USA (1994)
Hustadt, U., Motik, B., Sattler, U.: Data complexity of reasoning in very expressive description logics. In: IJCAI 2005. Proc. of the 19th Int. Joint Conf. on AI, Professional Book Center, pp. 466–471 (2005)
Kazakov, Y.: Saturation-based decision procedures for extensions of the guarded fragment, PhD thesis, University of Saarland (2005)
Krisnadhi, A.: Data complexity of instance checking in the \(\mathcal{EL}\) family of description logics. Master thesis, TU Dresden, Germany (2007)
Krisnadhi, A., Lutz, C.: Data complexity of instance checking in the \(\mathcal{EL}\) family of description logics. available from http://lat.inf.tu-dresden.de/~clu/papers/
Krötzsch, M., Rudolph, S., Hitzler, P.: On the complexity of horn description logics. In: Proc. of the 2nd WS on OWL: Experiences and Directions. CEUR-WS, vol. 216 (2006), http://ceur-ws.org/
Krötzsch, M., Rudolph, S.: Conjunctive Queries for \(\mathcal{EL}\) with Composition of Roles. In: DL 2007. Proc. of the 2007 Int. WS on DLs, CEUR-WS.org (2007)
Rosati, R.: On conjunctive query answering in \(\mathcal{EL}\). In: DL 2007. Proc. of the 2007 Int. WS on DLs, CEUR-WS.org (2007)
Schaerf, A.: On the complexity of the instance checking problem in concept languages with existential quantification. Journal of Intelligent Information Systems 2, 265–278 (1993)
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Krisnadhi, A., Lutz, C. (2007). Data Complexity in the \(\mathcal{EL}\) Family of Description Logics. In: Dershowitz, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2007. Lecture Notes in Computer Science(), vol 4790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75560-9_25
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DOI: https://doi.org/10.1007/978-3-540-75560-9_25
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