16 research outputs found
Querying Incomplete Data : Complexity and Tractability via Datalog and First-Order Rewritings
To answer database queries over incomplete data the gold standard is finding
certain answers: those that are true regardless of how incomplete data is
interpreted. Such answers can be found efficiently for conjunctive queries and
their unions, even in the presence of constraints. With negation added, the
problem becomes intractable however. We concentrate on the complexity of
certain answers under constraints, and on effficiently answering queries
outside the usual classes of (unions) of conjunctive queries by means of
rewriting as Datalog and first-order queries. We first notice that there are
three different ways in which query answering can be cast as a decision
problem. We complete the existing picture and provide precise complexity bounds
on all versions of the decision problem, for certain and best answers. We then
study a well-behaved class of queries that extends unions of conjunctive
queries with a mild form of negation. We show that for them, certain answers
can be expressed in Datalog with negation, even in the presence of functional
dependencies, thus making them tractable in data complexity. We show that in
general Datalog cannot be replaced by first-order logic, but without
constraints such a rewriting can be done in first-order. The paper is under
consideration in Theory and Practice of Logic Programming (TPLP).Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
Querying Data Exchange Settings Beyond Positive Queries
Data exchange, the problem of transferring data from a source schema to a
target schema, has been studied for several years.
The semantics of answering positive queries over the target schema has been
defined in early work, but little attention has been paid to more general
queries. A few proposals of semantics for more general queries exist but they
either do not properly extend the standard semantics under positive queries,
giving rise to counterintuitive answers, or they make query answering
undecidable even for the most important data exchange settings, e.g., with
weakly-acyclic dependencies.
The goal of this paper is to provide a new semantics for data exchange that
is able to deal with general queries. At the same time, we want our semantics
to coincide with the classical one when focusing on positive queries, and to
not trade-off too much in terms of complexity of query answering. We show that
query answering is undecidable in general under the new semantics, but it is
\co\NP\complete when the dependencies are weakly-acyclic.
Moreover, in the latter case, we show that exact answers under our semantics
can be computed by means of logic programs with choice, thus exploiting
existing efficient systems. For more efficient computations, we also show that
our semantics allows for the construction of a representative target instance,
similar in spirit to a universal solution, that can be exploited for computing
approximate answers in polynomial time. Under consideration in Theory and
Practice of Logic Programming (TPLP).Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
Games for query inseparability of description logic knowledge bases
We consider conjunctive query inseparability of description logic knowledge bases with respect to a given signature---a fundamental problem in knowledge base versioning, module extraction, forgetting and knowledge exchange. We give a uniform game-theoretic characterisation of knowledge base conjunctive query inseparability and develop worst-case optimal decision algorithms for fragments of Horn-ALCHI, including the description logics underpinning OWL 2 QL and OWL 2 EL. We also determine the data and combined complexity of deciding query inseparability. While query inseparability for all of these logics is P-complete for data complexity, the combined complexity ranges from P- to ExpTime- to 2ExpTime-completeness. We use these results to resolve two major open problems for OWL 2 QL by showing that TBox query inseparability and the membership problem for universal conjunctive query solutions in knowledge exchange are both ExpTime-complete for combined complexity. Finally, we introduce a more flexible notion of inseparability which compares answers to conjunctive queries in a given signature over a given set of individuals. In this case, checking query inseparability becomes NP-complete for data complexity, but the ExpTime- and 2ExpTime-completeness combined complexity results are preserved
Representability in DL-Lite_R Knowledge Base Exchange
Knowledge base exchange can be considered as a generalization of data exchange in which the aim is to exchange between a source and a target connected through mappings, not only explicit knowledge, i.e., data, but also implicit knowledge in the form of axioms. Such problem has been investigated recently using Description Logics (DLs) as representation formalism, thus assuming that the source and target KBs are given as a DL TBox+ABox, while the mappings have the form of DL TBox assertions. In this paper we are interested in the problem of representing a given source TBox by means of a target TBox that captures at best the intensional information in the source. In previous work, results on representability have been obtained for DL-LiteRDFS , a DL corresponding to the FOL fragment of RDFS. We extend these results to the positive fragment of DLLiteR, in which, differently from DL-LiteRDFS , the assertions in the TBox and the mappings may introduce existentially implied individuals. For this we need to overcome the challenge that the chase, a key notion in data and knowledge base exchange, is not guaranteed anymore to be finite
Knowledge base exchange: the case of OWL 2 QL
In this article, we define and study the problem of exchanging knowledge between a source and a target knowledge base (KB), connected through mappings. Differently from the traditional database exchange setting, which considers only the exchange of data, we are interested in exchanging implicit knowledge. As representation formalism we use Description Logics (DLs), thus assuming that the source and target KBs are given as a DL TBox+ABox, while the mappings have the form of DL TBox assertions. We define a general framework of KB exchange, and study the problem of translating the knowledge in the source KB according to the mappings expressed in OWL 2 QL, the profile of the standard Web Ontology Language OWL 2 based on the description logic DL-LiteR. We develop novel game- and automata-theoretic techniques, and we provide complexity results that range from NLogSpace to ExpTim