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    Deciding FO-rewritability of Regular Languages and Ontology-Mediated Queries in Linear Temporal Logic

    Kurucz, A. and Ryzhikov, Vladislav and Savateev, Yury and Zakhariyashchev, Michael (2023) Deciding FO-rewritability of Regular Languages and Ontology-Mediated Queries in Linear Temporal Logic. Journal of Artificial Intelligence Research 76 , ISSN 1076-9757.

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    Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some 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 prove that, similarly to known PSᴘᴀᴄᴇ-completeness of recognising FO(<)-definability of regular languages, deciding FO(<,≡)- and FO(<,MOD)-definability is also PSᴘᴀᴄᴇ-complete (unless ACC0 = NC1). We then use this result to show that deciding FO(<)-, FO(<,≡)- and FO(<,MOD)-rewritability of LTL OMQs is ExᴘSᴘᴀᴄᴇ-complete, and that these problems become PSᴘᴀᴄᴇ-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 PSᴘᴀᴄᴇ-, Π2p- and coNP-complete.


    Item Type: Article
    Keyword(s) / Subject(s): ontologies, semantic web, temporal reasoning, description logics
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Vladislav Ryzhikov
    Date Deposited: 23 Mar 2023 15:44
    Last Modified: 09 Aug 2023 12:54


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