This paper introduces a new logical formalism, intended for temporal conceptual modelling, as a natural combination of the well-known description logic DLR and point-based linear temporal logic with Since and Until. We define a query language (where queries are non-recursive Datalog programs and atoms are complex DLRUS expressions) and investigate the problem of checking query containment under the constraints defined by DLRUS conceptual schemas, as well as the problems of schema satisfiability and logical implication. Although it is shown that reasoning in full DLRUS is undecidable, we identify the decidable (in a sense, maximal) fragment DLR US by allowing applications of temporal operators to formulas and entities only (but not to relation expressions). We obtain the following hierarchy of complexity results: (a) reasoning in DLR US with atomic formulas is EXPTIME-complete, (b) satisfiability and logical implication of arbitrary DLR US formulas is EXPSPACE-complete, and (c) the problem of checking query containment of non-recursive Datalog queries under DLR US constraints is decidable in 2EXPTIME.

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@inproceedings{Artale2007TemporalDL, title={Temporal Description Logic}, author={Alessandro Artale and Enrico Franconi and Milenko Mosurovic and Frank Wolter and Michael Zakharyaschev}, year={2007} }