Abstract
We continue our investigation on nonmonotonic procedures for preferential Description Logics in order to reason about plausible but surprising scenarios. We consider an extension \(\mathcal {ALC}+\mathbf{T}_\mathbf{R}^{ \textsf {exp} }\) of the non-monotonic logic of typicality \(\mathcal {ALC}+\mathbf{T}_\mathbf{R}\) by inclusions of the form \(\mathbf{T}(C) \sqsubseteq _d D\), where d is a degree of expectedness. We consider a notion of extension of an ABox, in order to assume typicality assertions about individuals satisfying cardinality restrictions on concepts, then we define a preference relation among such extended ABoxes based on the degrees of expectedness, then we restrict entailment to those extensions that are minimal with respect to this preference relation. We propose a decision procedure for reasoning in \(\mathcal {ALC}+\mathbf{T}_\mathbf{R}^{ \textsf {exp} }\) and we exploit it to show that entailment is in ExpTime as for the underlying \(\mathcal {ALC}\). Last, we introduce a further extension of the proposed approach in order to reason about all plausible extensions of the ABox, by restricting the attention to specific degrees of expectedness ranging from the most surprising scenarios to the most expected ones.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In Theorem 10 in [13] the authors have shown that for any KB there exists a finite minimal canonical model of KB minimally satisfying the ABox.
- 2.
As mentioned, at this point of the presentation we only want to give an intuition of the inferences characterizing the logic \(\mathcal {ALC}+\mathbf{T}_\mathbf{R}^{ \textsf {exp} }\). Formal definitions of nonmonotonic entailment in \(\mathcal {ALC}+\mathbf{T}_\mathbf{R}^{ \textsf {exp} }\) will be provided in Definition 10.
- 3.
Other aggregation functions could be used to define \(d_i\) (e.g. maximun/minimum degree). We aim at studying the impact of this choice on the reasoning machinery in future research.
References
Bonatti, P.A., Lutz, C., Wolter, F.: The complexity of circumscription in DLs. J. Artif. Intell. Res.(JAIR) 35, 717–773 (2009)
Baader, F., Hollunder, B.: Priorities on defaults with prerequisites, and their application in treating specificity in terminological default logic. J. Autom. Reasoning (JAR) 15(1), 41–68 (1995)
Bonatti, P.A., Faella, M., Sauro, L.: Defeasible inclusions in low-complexity DLs. J. Artif. Intell. Res. (JAIR) 42, 719–764 (2011)
Donini, F.M., Nardi, D., Rosati, R.: Description logics of minimal knowledge and negation as failure. ACM Trans. Comput. Logics (ToCL) 3(2), 177–225 (2002)
Casini, G., Straccia, U.: Rational closure for defeasible description logics. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS (LNAI), vol. 6341, pp. 77–90. Springer, Heidelberg (2010). doi:10.1007/978-3-642-15675-5_9
Casini, G., Straccia, U.: Defeasible inheritance-based description logics. J. Artif. Intell. Res. (JAIR) 48, 415–473 (2013)
Straccia, U.: Default inheritance reasoning in hybrid kl-one-style logics. In: Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI 1993), pp. 676–681. Morgan Kaufmann (1993)
Bonatti, P.A., Faella, M., Petrova, I., Sauro, L.: A new semantics for overriding in description logics. Artif. Intell. 222, 1–48 (2015)
Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: ALC+T: a preferential extension of description logics. Fundam. Inform. 96, 341–372 (2009)
Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: A nonmonotonic description logic for reasoning about typicality. Artif. Intell. 195, 165–202 (2013)
Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: Preferential vs rational description logics: which one for reasoning about typicality? In: Coelho, H., Studer, R., Wooldridge, M. (eds.) Proceedings of the 19th European Conference on Artificial Intelligence (ECAI 2010). FAIA (Frontiers in Artificial Intelligence and Applications), Lisbon, Portugal, vol. 215, pp. 1069–1070. IOS Press (August (2010)
Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: Reasoning about typicality in low complexity DLs: the logics \(\cal{EL}^{\perp }{\bf T}_{min}\) and \(DL-Lite_{c}{\bf T}_{min}\). In: Walsh, T. (ed.) Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI 2011), Spain, pp. 894–899. IOS Press, Barcelona (2011)
Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: Semantic characterization of rational closure: from propositional logic to description logics. Artif. Intell. 226, 1–33 (2015)
Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44(1–2), 167–207 (1990)
Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? Artif. Intell. 55(1), 1–60 (1992)
Baader, F., Buchheit, M., Hollunder, B.: Cardinality restrictions on concepts. Artif. Intell. 88(1–2), 195–213 (1996)
Pozzato, G.L.: Preferential description logics meet sports entertainment: cardinality restrictions and perfect extensions for a better royal rumble match. In: Ancona, D., Maratea, M., Mascardi, V. (eds.) Proceedings of the 30th Italian Conference on Computational Logic CILC 2015. CEUR Workshop Proceedings, Genova, 1–3 July 2015, Italy, vol. 1459, pp. 159–174. CEUR-WS.org (2015)
Bordino, I., Mejova, Y., Lalmas, M.: Penguins in sweaters, or serendipitous entity search on user-generated content. In: He, Q., Iyengar, A., Nejdl, W., Pei, J., Rastogi, R. (eds.) 22nd ACM International Conference on Information and Knowledge Management, CIKM 2013, San Francisco, CA, USA, 27 October–1 November 2013, pp. 109–118 (2013)
Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.: The Description Logic Handbook - Theory, Implementation, and Applications, 2nd edn. Cambridge University Press, Cambridge (2010)
Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: Minimal model semantics and rational closure in description logics. In: Eiter, T., Glimm, B., Kazakov, Y., Krötzsch, M. (eds.) DL2016 Informal Proceedings of the 26th International Workshop on Description Logics. CEUR Workshop Proceedings, vol. 1014, pp. 168–180. CEUR-WS.org (2013)
Tobies, S.: The complexity of reasoning with cardinality restrictions and nominals in expressive description logics. J. Artif. Intell. Res. (JAIR) 12, 199–217 (2000)
Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: Rational closure in \(\cal{SHIQ}\). In: DL 2014, 27th International Workshop on Description Logics. CEUR Workshop Proceedings, vol. 1193, pp. 543–555. CEUR-WS.org (2014)
Acknowledgements
The author is partially supported by the project “ExceptionOWL: Nonmonotonic Extensions of Description Logics and OWL for defeasible inheritance with exceptions” by Università degli Studi di Torino and Compagnia di San Paolo, call 2014 “Excellent (young) PI”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Pozzato, G.L. (2016). Reasoning About Surprising Scenarios in Description Logics of Typicality. In: Adorni, G., Cagnoni, S., Gori, M., Maratea, M. (eds) AI*IA 2016 Advances in Artificial Intelligence. AI*IA 2016. Lecture Notes in Computer Science(), vol 10037. Springer, Cham. https://doi.org/10.1007/978-3-319-49130-1_31
Download citation
DOI: https://doi.org/10.1007/978-3-319-49130-1_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-49129-5
Online ISBN: 978-3-319-49130-1
eBook Packages: Computer ScienceComputer Science (R0)