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.
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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 \(\varTheta _2^P\).
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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.
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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
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