Aiming at ontology-based data access to temporal data, we design two-dimensional temporal ontology and query languages by combining logics from the (extended) DL-Lite family with linear temporal logic LTL over discrete time (Z,<). Our main concern is first-order rewritability of ontology-mediated queries (OMQs) that consist of a 2D ontology and a positive temporal instance query. Our target languages for FO-rewritings are two-sorted FO(<)—first-order logic with sorts for time instants ordered by the built-in precedence relation < and for the domain of individuals—its extension FO(<,≡) with the standard congruence predicates t ≡ 0 (mod n), for any fixed n > 1, and FO(RPR) that admits relational primitive recursion. In terms of circuit complexity, FO(<,≡)- and FO(RPR)-rewritability guarantee answering OMQs in uniform AC0 and NC1, respectively. We proceed in three steps. First, we define a hierarchy of 2D DL-Lite/LTL ontology languages and investigate the FO-rewritability of OMQs with atomic queries by constructing projections onto 1D LTL OMQs and employing recent results on the FO-rewritability of propositional LTL OMQs. As the projections involve deciding consistency of ontologies and data, we also consider the consistency problem for our languages. While the undecidability of consistency for 2D ontology languages with expressive Boolean role inclusions might be expected, we also show that, rather surprisingly, the restriction to Krom and Horn role inclusions leads to decidability (and ExpSpace-completeness), even if one admits full Booleans on concepts. As a final step, we lift some of the rewritability results for atomic OMQs to OMQs with expressive positive temporal instance queries. The lifting results are based on an in-depth study of the canonical models and only concern Horn ontologies.

SPARQL, a query language for RDF graphs, is one of the key technologies for the Semantic Web. The expressivity and complexity of various fragments of SPARQL have been studied extensively. It is usually assumed that the optional matching operator OPTIONAL has only two graph patterns as arguments. The specification of SPARQL, however, defines it as a ternary operator, with an additional filter condition. We address the problem of expressibility of the full ternary OPTIONAL via the simplified binary version and show that it is possible, but only with an exponential blowup in the size of the query (under common complexity-theoretic assumptions). We also study expressibility of other non-monotone SPARQL operators via optional matching and each other.

We advocate datalogMTL, a datalog extension of a Horn fragment of the metric temporal logic MTL, as a language for ontology-based access to temporal log data. We show that datalogMTL is EXPSPACE-complete even with punctual intervals, in which case MTL is known to be undecidable. Nonrecursive datalogMTL turns out to be PSPACE-complete for combined complexity and in AC0 for data complexity. We demonstrate by two real-world use cases that nonrecursive datalogMTL programs can express complex temporal concepts from typical user queries and thereby facilitate access to log data. Our experiments with Siemens turbine data and MesoWest weather data show that datalogMTL ontology-mediated queries are efficient and scale on large datasets of up to 11GB.

The key idea is that RDBMSs in practice appears to indicate only that answering data, 'stored in a standard relational database management real-world queries over real-world databases turns out to be system (RDBMS), can be queried through an OWL 2 QL tractable. As rewritings can turn a standard query to something ontology via a simple rewriting mechanism, i.e., by rewriting'out of this world,' a first rule of thumb could be as follows: the query into an SQL query that is then answered by the rewritten query should look similar to the original the RDBMS, without any changes to the data' (

We consider the setting of ontological database access, where an A-box is given in form of a relational database D and where a Boolean conjunctive query q has to be evaluated against D modulo a T-box Σ formulated in DL-Lite or Linear Datalog+/-. It is well-known that (Σ, q) can be rewritten into an equivalent nonrecursive Datalog program P that can be directly evaluated over D. However, for Linear Datalog+/- or for DL-Lite versions that allow for role inclusion, the rewriting methods described so far result in a nonrecursive Datalog program P of size exponential in the joint size of Σ and q . This gives rise to the interesting question whether such a rewriting necessarily needs to be of exponential size. In this paper we show that it is actually possible to translate (Σ, q ) into a polynomially sized equivalent nonrecursive Datalog program P.

In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PTL, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and computational realisability within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP- or PSPACE-complete.

The OWL 2 profile OWL 2 QL, based on the DL-Lite family of description logics, is emerging as a major language for developing new ontologies and approximating the existing ones. Its main application is ontology-based data access, where ontologies are used to provide background knowledge for answering queries over data. We investigate the corresponding notion of query inseparability (or equivalence) for OWL 2 QL ontologies and show that deciding query inseparability is PSPACE-hard and in EXPTIME. We give polynomial time (incomplete) algorithms and demonstrate by experiments that they can be used for practical module extraction.

Temporal conceptual data models (TCMs) can be encoded Conceptual data modelling formalisms such as the Entity-in various temporal description logics (TDLs), which Relationship model (ER) and Unified Modelling Language have been designed and investigated since the seminal paper (UML) have become a de facto standard in database design (Schild 1993) with the aim of understanding the computational by providing visual means to describe application domains price of introducing a temporal dimension in DLs; in a declarative and reusable way. On the other hand, both see (Lutz, Wolter, & Zakharyaschev 2008) for a recent survey. ER and UML turned out to be closely connected with description A general conclusion one can draw from the obtained logics (DLs) developed in the area of knowledge results is that--as far as there is nontrivial interaction between representation, underpinned by formal semantics and thus the temporal and DL components--TDLs based on capable of providing services for effective reasoning over full-fledged DLs like ALC turn out to be too complex for conceptual models; see, e.g., (Berardi, Calvanese, & De Giacomo effective reasoning (see the end of this section for details).

In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PTL, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and `computational realisability' within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP- or PSPACE-complete.