Abstract
Generalising the state of the art, an inconsistency-tolerant semantics can be seen as a couple composed of a modifier operator and an inference strategy. In this paper we deepen the analysis of such general setting and focus on two aspects. First, we investigate the rationality properties of such semantics for existential rule knowledge bases. Second, we unfold the broad landscape of complexity results of inconsistency-tolerant semantics under a specific (yet expressive) subclass of existential rules.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For readability, we restrict our focus to Boolean conjunctive queries, however the framework and the obtained results can be directly extended to general conjunctive queries.
- 2.
Note however that CAR and ICAR [16] are close to \(\langle \mathsf {RC},\forall \rangle \) and \(\langle \mathsf {RC}, \cap \rangle \) resp., but not equivalent. They could be covered by considering other elementary modifiers.
- 3.
Most examples in this section are provided in DL-Lite\(_{\mathcal R}\) in order to show that some rationality properties do not hold even in this simple fragment of existential rules.
- 4.
This example also shows that CAR and ICAR [16] do not satisfy ConsS (although they do when the conclusion is a single atom).
- 5.
We have adopted here a formulation close to the one of KLM logical properties, even at the cost of simplicity. For instance \(\langle {\mathcal {T}},{\mathcal {A}}_{\alpha }\rangle \models \langle {\mathcal {T}},{\mathcal {A}}_{\beta }\rangle \) could have been simplified in \(\langle {\mathcal {T}},{\mathcal {A}}_{\alpha }\rangle \models {\mathcal {A}}_{\beta }\). We remind that \(\models \) and \(\equiv \) denote standard logical entailment and equivalence.
- 6.
This complexity measure is usually considered for query answering problems. Only the data (here the ABox) are considered in the problem input.
- 7.
PP includes NP, co-NP and \(\varTheta _2^P\).
References
Arenas, M., Bertossi, L.E., Chomicki, J.: Consistent query answers in inconsistent databases. In: Proceedings of the Eighteenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pp. 68–79 (1999)
Baget, J.-F., Benferhat, S., Bouraoui, Z., Croitoru, M., Mugnier, M.-L., Papini, O., Rocher, S., Tabia, K.: A general modifier-based framework for inconsistency-tolerant query answering. In: Proceedings of the Fifteenth International Conference on Principles of Knowledge Representation and Reasoning, KR (2016)
Baget, J.-F., Leclère, M., Mugnier, M.-L., Salvat, E.: On rules with existential variables: Walking the decidability line. Artif. Intell. 175(9–10), 1620–1654 (2011)
Benferhat, S., Bouraoui, Z., Croitoru, M., Papini, O., Tabia, K.: Non-objection inference for inconsistency-tolerant query answering. In: Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence (2016)
Benferhat, S., Cayrol, C., Dubois, D., Lang, J., Prade, H.: Inconsistency management and prioritized syntax-based entailment. In: Proceedings of the 13th International Joint Conference on Artificial Intelligence, pp. 640–647 (1993)
Bienvenu, M.: On the complexity of consistent query answering in the presence of simple ontologies. In: Proceedings of the Twenty-Sixth Conference on Artificial Intelligence (2012)
Bienvenu, M., Bourgaux, C., Goasdoué, F.: Querying inconsistent description logic knowledge bases under preferred repair semantics. In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, pp. 996–1002 (2014)
Calì, A., Gottlob, G., Pieris, A.: Towards more expressive ontology languages: the query answering problem. Artif. Intell. 193, 87–128 (2012)
Calì, A., Gottlob, G., Lukasiewicz, T.: A general datalog-based framework for tractable query answering over ontologies. J. Web Sem. 14, 57–83 (2012)
Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: the DL-Lite family. J. Autom. Reason. 39(3), 385–429 (2007)
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
Gärdenfors, P., Makinson, D.: Nonmonotonic inference based on expectations. Artif. Intell. 65(2), 197–245 (1994)
Gill, J.: Computational complexity of probabilistic turing machines. SIAM J. Comput. 6(4), 675–695 (1977)
Kraus, S., Lehmann, D.J., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44(1–2), 167–207 (1990)
Lembo, D., Lenzerini, M., Rosati, R., Ruzzi, M., Savo, D.F.: Inconsistency-tolerant semantics for description logics. In: Hitzler, P., Lukasiewicz, T. (eds.) RR 2010. LNCS, vol. 6333, pp. 103–117. Springer, Heidelberg (2010). doi:10.1007/978-3-642-15918-3_9
Lembo, D., Lenzerini, M., Rosati, R., Ruzzi, M., Savo, D.F.: Inconsistency-tolerant query answering in ontology-based data access. J. Web Sem. 33, 3–29 (2015)
Lenzerini, M.: Ontology-based data management. In: Proceedings of the 6th Alberto Mendelzon International Workshop on Foundations of Data Management 2012, pp. 12–15 (2012)
Poggi, A., Lembo, D., Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Linking data to ontologies. J. Data Semant. 10, 133–173 (2008)
Acknowledgments
This work was supported by the projects ASPIQ (ANR-12-BS02-0003), PAGOGA (ANR-12-JS02-007-01) and the ERC Starting Grant 637277.
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
Baget, J.F. et al. (2016). Inconsistency-Tolerant Query Answering: Rationality Properties and Computational Complexity Analysis. In: Michael, L., Kakas, A. (eds) Logics in Artificial Intelligence. JELIA 2016. Lecture Notes in Computer Science(), vol 10021. Springer, Cham. https://doi.org/10.1007/978-3-319-48758-8_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-48758-8_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48757-1
Online ISBN: 978-3-319-48758-8
eBook Packages: Computer ScienceComputer Science (R0)