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Deciding FO-Rewritability of Ontology-Mediated Queries in Linear Temporal Logic

Authors Vladislav Ryzhikov, Yury Savateev, Michael Zakharyaschev

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ACM Subject Classification
  • Theory of computation → Modal and temporal logics
Keywords
  • Linear temporal logic
  • ontology-mediated query
  • first-order rewritability

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Abstract

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 in AC⁰, ACC⁰ and NC¹ coincides with FO(<,≡)-rewritability using unary predicates x ≡ 0 (mod n), FO(<,MOD)-rewritability, and FO(RPR)-rewritability using relational primitive recursion, respectively. We then show that deciding FO(<)-, FO(<,≡)- and FO(<,MOD)-rewritability of LTL OMQs is ExpSpace-complete, and that these problems become PSpace-complete for OMQs with a linear Horn ontology and an atomic query, and also a positive query in the cases of FO(<)- and FO(<,≡)-rewritability. Further, we consider FO(<)-rewritability of OMQs with a binary-clause ontology and identify OMQ classes, for which deciding it is PSpace-, Π₂^p- and coNP-complete.

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Vladislav Ryzhikov, Yury Savateev, and Michael Zakharyaschev. Deciding FO-Rewritability of Ontology-Mediated Queries in Linear Temporal Logic. In 28th International Symposium on Temporal Representation and Reasoning (TIME 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 206, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.TIME.2021.10

Author Details

Vladislav Ryzhikov
  • Department of Computer Science, Birkbeck, University of London, UK
Yury Savateev
  • Department of Computer Science, Birkbeck, University of London, UK
  • HSE University, Moscow, Russia
Michael Zakharyaschev
  • Department of Computer Science, Birkbeck, University of London, UK
  • HSE University, Moscow, Russia

Funding

This work was supported by the UK EPSRC grant EP/S032282.

Acknowledgements

The open access publication of this article was supported by the Alpen-Adria-Universität Klagenfurt, Austria.

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