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Aiming at ontology-based data access to temporal data, we designtwo-dimensional temporal ontology and query languages by combining logics fromthe (extended) DL-Lite family with linear temporal logic LTL over discrete time(Z,<). Our main concern is first-order rewritability of ontology-mediatedqueries (OMQs) that consist of a 2D ontology and a positive temporal instancequery. Our target languages for FO-rewritings are two-sorted FO(<) -first-order logic with sorts for time instants ordered by the built-inprecedence relation < and for the domain of individuals - its extension FOEwith the standard congruence predicates t \equiv 0 mod n, for any fixed n > 1,and FO(RPR) that admits relational primitive recursion. In terms of circuitcomplexity, FOE- and FO(RPR)-rewritability guarantee answering OMQs in uniformAC0 and NC1, respectively.  We proceed in three steps. First, we define a hierarchy of 2D DL-Lite/LTLontology languages and investigate the FO-rewritability of OMQs with atomicqueries by constructing projections onto 1D LTL OMQs and employing recentresults on the FO-rewritability of propositional LTL OMQs. As the projectionsinvolve deciding consistency of ontologies and data, we also consider theconsistency problem for our languages. While the undecidability of consistencyfor 2D ontology languages with expressive Boolean role inclusions might beexpected, we also show that, rather surprisingly, the restriction to Krom andHorn role inclusions leads to decidability (and ExpSpace-completeness), even ifone admits full Booleans on concepts. As a final step, we lift some of therewritability results for atomic OMQs to OMQs with expressive positive temporalinstance queries. The lifting results are based on an in-depth study of thecanonical models and only concern Horn ontologies.

First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries