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    First-order rewritability of ontology-mediated queries in linear temporal logic

    Artale, A. and Kontchakov, Roman and Kovtunova, A. and Ryzhikov, Vladislav and Wolter, F. and Zakhariyashchev, Michael (2021) First-order rewritability of ontology-mediated queries in linear temporal logic. Artificial Intelligence 299 , ISSN 0004-3702.

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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 (Z; <). Queries are given in LTL or MFO(<), 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 used in the ontology and distinguishing between ontologies given in full LTL and its core, Krom and Horn fragments, we identify a hierarchy of OMQs with atomic queries by proving rewritability into either FO(<), first-order logic with the built-in linear order, or FO(<, \equiv), which extends FO(<) with the standard arithmetic predicates x \equiv 0 (mod n), for any fixed n > 1, or FO(RPR), which extends FO(<) with relational primitive recursion. In terms of circuit complexity, FO(<, \equiv)- and FO(RPR)-rewritability guarantee OMQ answering in uniform AC0 and, respectively, NC1. We obtain similar hierarchies for more expressive types of queries: positive LTL-formulas, monotone MFO(<)- and arbitrary MFO(<)-formulas. Our results are directly applicable if the temporal data to be accessed is one-dimensional; moreover, they lay foundations for investigating ontology-based access using combinations of temporal and description logics over two-dimensional temporal data.


    Item Type: Article
    Keyword(s) / Subject(s): Linear temporal logic, Description logic, Ontology-based data access, First-order rewritability, Data complexity
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Roman Kontchakov
    Date Deposited: 28 Jun 2021 08:47
    Last Modified: 09 Aug 2023 12:51


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