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A tetrachotomy of ontology-mediated queries with a covering axiom
Artificial Intelligence. 2022. Vol. 309. Article 103738.
Gerasimova O., Kikot S., Podolskii V. V., Kurucz A., Zakharyaschev M.
Our concern is the problem of efficiently determining the data complexity of answering queries mediated by description logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology-based data access and datalog optimisation, this problem is known to be computationally very complex in general, with no explicit syntactic characterisations available. In this article, aiming to understand the fundamental roots of this difficulty, we strip the problem to the bare bones and focus on Boolean conjunctive queries mediated by a simple covering axiom stating that one class is covered by the union of two other classes. We show that, on the one hand, these rudimentary ontology-mediated queries, called disjunctive sirups (or d-sirups), capture many features and difficulties of the general case. For example, answering d-sirups is Π2p-complete for combined complexity and can be in Image 1 or L-, NL-, P-, or coNP-complete for data complexity (with the problem of recognising FO-rewritability of d-sirups being 2ExpTime-hard); some d-sirups only have exponential-size resolution proofs, some only double-exponential-size positive existential FO-rewritings and single-exponential-size nonrecursive datalog rewritings. On the other hand, we prove a few partial sufficient and necessary conditions of FO- and (symmetric/linear-) datalog rewritability of d-sirups. Our main technical result is a complete and transparent syntactic Image 1/NL/P/coNP tetrachotomy of d-sirups with disjoint covering classes and a path-shaped Boolean conjunctive query. To obtain this tetrachotomy, we develop new techniques for establishing P- and coNP-hardness of answering non-Horn ontology-mediated queries as well as showing that they can be answered in NL.
Publication based on the results of:
Joulitov A.K., Lomazova I.A., Proceedings of the Institute for System Programming of the RAS 2026 Vol. 38 No. 4(2) P. 215–224
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Самарин А. В., Торопов А. Г., Савельев А. Г. et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 4 P. 1044–1052
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Added: September 21, 2026
Tomat A., Sergei O. Kuznetsov, International Journal of Approximate Reasoning 2026 Vol. 197 Article 109754
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Aleksei Samarin, Nazarenko A., Kotenko E. et al., / Series arXiv "math". 2025. No. 2511.20141.
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Buzmakov A. V., Dudyrev E., Kuznetsov S. et al., International Journal of Approximate Reasoning 2024 Vol. 165 Article 109084
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Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) given in linear temporal logic LTL over (Z, <) and deciding whether it is rewritable to an FO(<)-query, possibly with extra predicates. First, we observe that, in line with the circuit complexity and FO-definability of regular languages, OMQ answering ...
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We investigate ontology-based data access to temporal data. We consider temporal ontologies given in linear temporal logic LTL interpreted over discrete time . Queries are given in LTL or , monadic first-order logic with a built-in linear order. Our concern is first-order rewritability of ontology-mediated queries (OMQs) consisting of a temporal ontology and a query. By taking account of the temporal operators ...
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Added: October 29, 2019
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It has recently been shown that first-order- and datalog-rewritability of ontology-mediated queries (OMQs) with expressive ontologies can be checked in NExpTime using a reduction to CSPs. In this paper, we present a case study for OMQs with Boolean conjunctive queries and a fixed ontology consisting of a single covering axiom 𝐴 -> 𝐹 v 𝑇, A -> F v T, possibly supplemented with ...
Added: July 29, 2019
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This Festschrift has been put together on the occasion of Franz Baader's 60th birthday to celebrate his fundamental and highly influential scientific contributions. The 30 papers in this volume cover several scientific areas that Franz Baader has been working on during the last three decades, including description logics, term rewriting, and the combination of decision procedures. We hope that ...
Added: July 29, 2019