DL-lite with attributes and datatypes

We extend the DL-Lite languages by means of attributes and datatypes. Attributes -- a notion borrowed from data models -- associate concrete values from datatypes to abstract objects and in this way complement roles, which describe relationships between abstract objects. The extended languages remain tractable (with a notable exception) even though they contain both existential and (a limited form of) universal quantification. We present complexity results for two most important reasoning problems in DL-Lite: combined complexity of knowledge base satisfiability and data complexity of positive existential query answering

Conjunctive query inseparability in OWL2QL is ExpTime-hard

We settle an open question on the complexity of the following problem: given two OWL2QL TBoxes and a signature, decide whether these TBoxes return the same answers to any conjunctive query over any data formulated in the given signature. It has been known that the complexity of this problem is between PSpace and ExpTime. Here we show that the problem is ExpTime-complete and, in fact, deciding whether two OWL2QL knowledge bases (each with its own data) give the same answers to any conjunctive query is ExpTime-hard

A cookbook for temporal conceptual data modelling with description logic

We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. In the temporal dimension, they capture future and past temporal operators on concepts, flexible and rigid roles, the operators `always' and `some time' on roles, data assertions for particular moments of time and global concept inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (Z,<), satisfying the constant domain assumption. We prove that the most expressive of our temporal description logics (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turn out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions we obtain logics whose complexity ranges between PSpace and NLogSpace. These positive results were obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models

Query inseparability by games

We investigate conjunctive query inseparability of description logic knowledge bases (KBs) with respect to a given signature, a fundamental problem for KB versioning, module extraction, forgetting and knowledge exchange. We develop a game-theoretic technique for checking query inseparability of KBs expressed in fragments of Horn-ALCHI, and show a number of complexity results ranging from P to ExpTime and 2ExpTime. We also employ our results to resolve two major open problems for OWL 2 QL by showing that TBox query inseparability and the membership problem for universal UCQ-solutions in knowledge exchange are both ExpTime-complete for combined complexity