In this article, aiming to understand the fundamental roots of this difficulty, we strip the problem to the bare bones and focus on Boolean conjunctive queries mediated by a simple covering axiom stating that one class is covered by the union of two other classes.
We investigate the data complexity of answering queries mediated by metric temporal logic ontologies under the event-based semantics assuming that data instances are finite timed words timestamped with binary fractions.
We also consider the problem whether two ALC TBoxes give the same answers to any query over any ABox in a given signature and show that, for CQs, this problem is undecidable, too.
The question whether an ontology can safely be replaced by another, possibly simpler, one is fundamental for many ontology engineering and maintenance tasks.
We give solutions to two fundamental computational problems in ontology-based data access with the W3C standard ontology language OWL 2 QL: the succinctness problem for first-order rewritings of ontology-mediated queries (OMQs), and the complexity problem for OMQ answering.
We also consider the problem whether two ALC TBoxes give the same answers to any query in a given vocabulary over all ABoxes, and show that for CQs this problem is undecidable, too, but becomes decidable and 2EXPTIME-complete in Horn-ALC, and even EXPTIME-complete in Horn-ALC when restricted to (unions of) rooted CQs.
Logic in Computer Science
The recently introduced series of description logics under the common moniker DL-Lite has attracted attention of the description logic and semantic web communities due to the low computational complexity of inference, on the one hand, and the ability to represent conceptual modeling formalisms, on the other.
Our aim is to investigate ontology-based data access over temporal data with validity time and ontologies capable of temporal conceptual modelling.
We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity.