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 (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(<,≡), which extends FO(<) with the standard arithmetic predicates x≡0(modn), for any fixed n>1, or FO(RPR), which extends FO(<) with relational primitive recursion. In terms of circuit complexity, FO(<,≡)- and FO(RPR)-rewritability guarantee OMQ answering in uniform Image 1 and, respectively, Image 2.