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Inconsistency-Tolerant Instance Checking in Tractable Description Logics

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Rules and Reasoning (RuleML+RR 2017)

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Abstract

Research on inconsistency-tolerant query answering usually assumes that the terminological knowledge is correct, and only the facts (ABox) need to be repaired. In this paper we study the problem of answering instance queries over inconsistent ontologies, by repairing the whole knowledge base (KB). Contrary to ABox repairs, when KB repairs are considered, instance checking in \(\textit{DL}\text {-}{} \textit{Lite}_\textit{Horn}\) w.r.t. the brave semantics remains tractable, and the intersection semantics allow for an any-time algorithm. We also show that inconsistency-tolerant instance checking w.r.t. ABox repairs is intractable even if only polynomially many ABox repairs exist.

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Notes

  1. 1.

    A hitting set for e.g. \(\mathsf {Rep}_{\mathcal {K}}\) is a set \(\mathcal {S} \) that satisfies \(\mathcal {S} \cap \mathcal {R} \not =\emptyset \) for every \(\mathcal {R} \in \mathsf {Rep}_{\mathcal {K}} \).

  2. 2.

    Throughout this section, \(\mathsf {Rep}_{\mathcal {K}}\) denotes the set of all ABox repairs.

  3. 3.

    For simplicity, we identify a propositional valuation \(\mathcal {V}\) with the set of variables that it makes true.

  4. 4.

    One can think of this problem as the dual of the one considered in the proof of Theorem 9.

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Peñaloza, R. (2017). Inconsistency-Tolerant Instance Checking in Tractable Description Logics. In: Costantini, S., Franconi, E., Van Woensel, W., Kontchakov, R., Sadri, F., Roman, D. (eds) Rules and Reasoning. RuleML+RR 2017. Lecture Notes in Computer Science(), vol 10364. Springer, Cham. https://doi.org/10.1007/978-3-319-61252-2_15

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