Horn rewritability vs PTime query evaluation for description logic TBoxes

We study the following question: if τ is a TBox that is formulated in an expressive DL L and all CQs can be evaluated in PTime w.r.t. τ, can τ be replaced by a TBox τ' that is formulated in the Horn-fragment of L and such that for all CQs and ABoxes, the answers w.r.t. τ and τ' coincide? Our main results are that this is indeed the case when L is the set of ALCHI or ALCIF TBoxes of quantifier depth 1 (which covers the majority of such TBoxes), but not for ALCHIF and ALCQ TBoxes of depth 1

Answering Non-Monotonic Queries in Relational Data Exchange

Relational data exchange is the problem of translating relational data from a source schema into a target schema, according to a specification of the relationship between the source data and the target data. One of the basic issues is how to answer queries that are posed against target data. While consensus has been reached on the definitive semantics for monotonic queries, this issue turned out to be considerably more difficult for non-monotonic queries. Several semantics for non-monotonic queries have been proposed in the past few years. This article proposes a new semantics for non-monotonic queries, called the GCWA*-semantics. It is inspired by semantics from the area of deductive databases. We show that the GCWA*-semantics coincides with the standard open world semantics on monotonic queries, and we further explore the (data) complexity of evaluating non-monotonic queries under the GCWA*-semantics. In particular, we introduce a class of schema mappings for which universal queries can be evaluated under the GCWA*-semantics in polynomial time (data complexity) on the core of the universal solutions.Comment: 55 pages, 3 figure

Constraint patterns for tractable ontology-mediated queries with datatypes

Adding datatypes to ontology-mediated conjunctive queries (OMQs) often makes query answering hard. This applies, in particular, to datatypes with non-unary predicates. In this paper we propose a new, non-uniform way, of analysing the data-complexity of OMQ answering with datatypes containing higher-arity predicates. We aim at a classification of the patterns of datatype atoms in OMQs into those that can occur in non-tractable OMQs and those that only occur in tractable OMQs. Our main result is a P/coNP-dichotomy for OMQs over DL-Lite TBoxes and rooted CQs using the datatype (ℚ, ≤). The proof employs a recent dichotomy result by Bodirsky and Kara for temporal constraint satisfaction problems

Logic and data exchange: Which solutions are “good” solutions

This paper gives an introduction into the area of data exchange, with a special emphasis on the question of which solutions can be considered “good ” solutions. We will concentrate on notions of “good” solutions for query answering, in particular, universal solutions, the core of the universal solutions, and CWA-solutions.