First-order rewritability of ontology-mediated queries in linear temporal logic
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 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 , first-order logic with the built-in linear order, or , which extends with the standard arithmetic predicates , for any fixed , or , which extends with relational primitive recursion. In terms of circuit complexity, - and -rewritability guarantee OMQ answering in uniform and, respectively, .
We obtain similar hierarchies for more expressive types of queries: positive LTL-formulas, monotone - and arbitrary -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.