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An ASP approach for reasoning in a concept-aware multipreferential lightweight DL

Published online by Cambridge University Press:  21 September 2020

Laura GiordanoOpen the ORCID record for Laura Giordano[Opens in a new window] and
Daniele Theseider Dupré
Laura Giordano
Affiliation:
DISIT, Università del Piemonte Orientale, Italy (e-mail: laura.giordano@uniupo.it, dtd@uniupo.it)
Daniele Theseider Dupré
Affiliation:
DISIT, Università del Piemonte Orientale, Italy (e-mail: laura.giordano@uniupo.it, dtd@uniupo.it)
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Abstract

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In this paper we develop a concept aware multi-preferential semantics for dealing with typicality in description logics, where preferences are associated with concepts, starting from a collection of ranked TBoxes containing defeasible concept inclusions. Preferences are combined to define a preferential interpretation in which defeasible inclusions can be evaluated. The construction of the concept-aware multipreference semantics is related to Brewka’s framework for qualitative preferences. We exploit Answer Set Programming (in particular, asprin) to achieve defeasible reasoning under the multipreference approach for the lightweight description logic ξ$\mathcal L_ \bot ^ + $.

Keywords

Nonmonotonic ReasoningDescription LogicsPreferencesASP

Information

Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 20 , Issue 5: 36th International Conference on Logic Programming Special Issue I , September 2020, pp. 751 - 766
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

References

Baader, F., Brandt, S., and Lutz, C. 2005. Pushing the envelope. In Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), Kaelbling, L. and Saffiotti, A., Eds. Professional Book Center, Edinburgh, Scotland, UK, 364–369.Google Scholar
Baader, F. and Hollunder, B. 1995. Embedding defaults into terminological knowledge representation formalisms. J. Autom. Reasoning 14, 1, 149–180.Google Scholar
Beierle, C., Eichhorn, C., Kern-Isberner, G., and Kutsch, S. 2018. Properties of skeptical c-inference for conditional knowledge bases and its realization as a constraint satisfaction problem. Ann. Math. Artif. Intell. 83, 3-4, 247–275.CrossRefGoogle Scholar
Bonatti, P. A. 2019. Rational closure for all description logics. Artif. Intell. 274, 197–223.CrossRefGoogle Scholar
Bonatti, P. A., Faella, M., Petrova, I., and Sauro, L. 2015. A new semantics for overriding in description logics. Artif. Intell. 222, 1–48.Google Scholar
Bonatti, P. A., Faella, M., and Sauro, L. 2011. Defeasible inclusions in low-complexity dls. J. Artif. Intell. Res. (JAIR) 42, 719–764.Google Scholar
Bonatti, P. A., Lutz, C., and Wolter, F. 2009. The Complexity of Circumscription in DLs. Journal of Artificial Intelligence Research (JAIR) 35, 717–773.Google Scholar
Bonatti, P. A., Petrova, I. M., and Sauro, L. 2015. Optimizing the computation of overriding. In Proc. ISWC 2015. 356–372.Google Scholar
Bozzato, L., Eiter, T., and Serafini, L. 2014. Contextualized knowledge repositories with justifiable exceptions. In DL 2014. CEUR Workshop Proceedings, vol. 1193. 112–123.Google Scholar
Bozzato, L., Eiter, T., and Serafini, L. 2018. Enhancing context knowledge repositories with justifiable exceptions. Artif. Intell. 257, 72–126.CrossRefGoogle Scholar
Brewka, G. 1989. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of the 11th International Joint Conference on Artificial Intelligence. Detroit, MI, USA, August 1989. 1043–1048.Google Scholar
Brewka, G. 2004. A rank based description language for qualitative preferences. In Proceedings of the 16th Eureopean Conference on Artificial Intelligence, ECAI’2004, Valencia, Spain, August 22-27, 2004. 303–307.Google Scholar
Brewka, G., Delgrande, J. P., Romero, J., and Schaub, T. 2015. asprin: Customizing answer set preferences without a headache. In Proc. AAAI 2015. 1467–1474.Google Scholar
Britz, K., Heidema, J., and Meyer, T. 2008. Semantic preferential subsumption. In Principles of Knowledge Representation and Reasoning: Proceedings of the 11th International Conference (KR 2008), Brewka, G. and Lang, J., Eds. AAAI Press, Sidney, Australia, 476–484.Google Scholar
Casini, G., Meyer, T., Varzinczak, I. J. ,, and Moodley, K. 2013. Nonmonotonic Reasoning in Description Logics: Rational Closure for the ABox. In 26th International Workshop on Description Logics (DL 2013). CEUR Workshop Proceedings, vol. 1014. 600–615.Google Scholar
Casini, G. and Straccia, U. 2010. Rational Closure for Defeasible Description Logics. In Proc. 12th European Conf. on Logics in Artificial Intelligence (JELIA 2010), Janhunen, T. and Niemelä, I., Eds. LNCS, vol. 6341. Springer, Helsinki, Finland, 77–90.Google Scholar
Casini, G. and Straccia, U. 2013. Defeasible inheritance-based description logics. Journal of Artificial Intelligence Research (JAIR) 48, 415–473.Google Scholar
Casini, G., Straccia, U., and Meyer, T. 2019. A polynomial time subsumption algorithm for nominal safe elo under rational closure. Inf. Sci. 501, 588–620.Google Scholar
Deane, G., Broda, K., and Russo, A. 2015. Reasoning in the presence of inconsistency through preferential ALC. In 20th International Conferences on Logic for Programming, Artificial Intelligence and Reasoning, LPAR 2015, Suva, Fiji, November 24-28, 2015. 67–80.Google Scholar
Donini, F. M., Nardi, D., and Rosati, R. 2002. Description logics of minimal knowledge and negation as failure. ACM Transactions on Computational Logic (ToCL) 3, 2, 177–225.Google Scholar
Eiter, T. and Gottlob, G. 1995. On the computational cost of disjunctive logic programming: Propositional case. Annals of Mathematics and Artificial Intelligence 15, 3-4, 289–323.Google Scholar
Eiter, T., Ianni, G., Lukasiewicz, T., and Schindlauer, R. 2011. Well-founded semantics for description logic programs in the semantic web. ACM Trans. Comput. Log. 12, 2, 11.Google Scholar
Eiter, T., Ianni, G., Lukasiewicz, T., Schindlauer, R., and Tompits, H. 2008. Combining answer set programming with description logics for the semantic web. Artif. Intell. 172, 12-13, 1495–1539.Google Scholar
Gil, O. F. 2014. On the Non-Monotonic Description Logic ALC+Tmin CoRR abs/1404.6566.Google Scholar
Giordano, L., Gliozzi, V., and Olivetti, N. 2018. Towards a rational closure for expressive description logics: the case of SHIQ . Fundam. Inform. 159, 1-2, 95–122.Google Scholar
Giordano, L., Gliozzi, V., Olivetti, N., and Pozzato, G. 2013. Minimal Model Semantics and Rational Closure in Description Logics. In 26th International Workshop on Description Logics (DL 2013). Vol. 1014. 168–180.Google Scholar
Giordano, L., Gliozzi, V., Olivetti, N., and Pozzato, G. L. 2007. Preferential Description Logics. In Proc. LPAR 2007 (14th Conf. on Logic for Programming, Artificial Intelligence, and Reasoning), Dershowitz, N. and Voronkov, A., Eds. LNAI, vol. 4790. Springer-Verlag, 257–272.Google Scholar
Giordano, L., Gliozzi, V., Olivetti, N., and Pozzato, G. L. 2011. Reasoning about typicality in low complexity DLs: the logics Tmin and DL–Litec In Proc. 22nd Int. Joint Conf. on Artificial Intelligence (IJCAI 2011). Morgan Kaufmann, Barcelona, 894–899.Google Scholar
Giordano, L. and Theseider Dupré, D. 2016. ASP for minimal entailment in a rational extension of SROEL. TPLP 16, 5-6, 738–754.Google Scholar
Giordano, L. and Theseider Dupré, D. 2018. Defeasible Reasoning in SROEL from Rational Entailment to Rational Closure. Fundam. Inform. 161, 1-2, 135–161.Google Scholar
Giordano, L. and Theseider Dupré, D. 2020. An ASP approach for reasoning in a concept-aware multipreferential lightweight DL. CoRR abs/2006.04387.CrossRefGoogle Scholar
Gliozzi, V. 2016. Reasoning about multiple aspects in rational closure for DLs. In Proc. AIIA 2016, Genova, Italy, Nov 29 - Dec 1, 2016. LNCS, vol. 10037. 392–405.Google Scholar
Gottlob, G., Hernich, A., Kupke, C., and Lukasiewicz, T. 2014. Stable model semantics for guarded existential rules and description logics. In Proc. 14th Int. Conf. on Principles of Knowledge Representation and Reasoning, KR 2014, Vienna, Austria, July 20-24.Google Scholar
Kazakov, Y., Krötzsch, M., and Simancik, F. 2014. The incredible ELK. J. Autom. Reasoning 53, 1, 1–61.Google Scholar
Knorr, M., Hitzler, P., and Maier, F. 2012. Reconciling OWL and non-monotonic rules for the semantic web. In ECAI 2012. 474–479.Google Scholar
Kraus, S., Lehmann, D., and Magidor, M. 1990. Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44, 1-2, 167–207.CrossRefGoogle Scholar
Krötzsch, M. 2010. Efficient inferencing for OWL EL. In Proc. JELIA 2010. 234–246.CrossRefGoogle Scholar
Lehmann, D. and Magidor, M. 1992. What does a conditional knowledge base entail? Artificial Intelligence 55, 1, 1–60.Google Scholar
Lehmann, D. J. 1995. Another perspective on default reasoning. Ann. Math. Artif. Intell. 15, 1, 61–82.Google Scholar
Lieto, A. and Pozzato, G. 2018. A description logic of typicality for conceptual combination. In Proc. ISMIS 2018, Cyprus, October 29-31, 2018. LNCS, vol. 11177. Springer, 189–199.Google Scholar
Motik, B. and Rosati, R. 2010. Reconciling Description Logics and rules. J. ACM 57, 5.Google Scholar
Pearl, J. 1990. System Z: A Natural Ordering of Defaults with Tractable Applications to Nonmonotonic Reasoning. In TARK (3rd Conference on Theoretical Aspects of Reasoning about Knowledge), R. Parikh, Ed. Kaufmann, Morgan, Pacific Grove, CA, USA, 121–135.Google Scholar
Pensel, M. and Turhan, A. 2018. Reasoning in the defeasible description logic EL- computing standard inferences under rational and relevant semantics. J. Approx. Reasoning 103, 28–70.Google Scholar
Straccia, U. 1993. Default inheritance reasoning in hybrid KL-ONE-Style Logics. In Proc. 13th Int. Joint Conf. on Artificial Intelligence (IJCAI 1993). Chambéry, France, 676–681.Google Scholar