743 research outputs found
The Logic of Counting Query Answers
We consider the problem of counting the number of answers to a first-order
formula on a finite structure. We present and study an extension of first-order
logic in which algorithms for this counting problem can be naturally and
conveniently expressed, in senses that are made precise and that are motivated
by the wish to understand tractable cases of the counting problem
Inconsistency-tolerant Query Answering in Ontology-based Data Access
Ontology-based data access (OBDA) is receiving great attention as a new paradigm for managing information systems through semantic technologies. According to this paradigm, a Description Logic ontology provides an abstract and formal representation of the domain of interest to the information system, and is used as a sophisticated schema for accessing the data and formulating queries over them. In this paper, we address the problem of dealing with inconsistencies in OBDA. Our general goal is both to study DL semantical frameworks that are inconsistency-tolerant, and to devise techniques for answering unions of conjunctive queries under such inconsistency-tolerant semantics. Our work is inspired by the approaches to consistent query answering in databases, which are based on the idea of living with inconsistencies in the database, but trying to obtain only consistent information during query answering, by relying on the notion of database repair. We first adapt the notion of database repair to our context, and show that, according to such a notion, inconsistency-tolerant query answering is intractable, even for very simple DLs. Therefore, we propose a different repair-based semantics, with the goal of reaching a good compromise between the expressive power of the semantics and the computational complexity of inconsistency-tolerant query answering. Indeed, we show that query answering under the new semantics is first-order rewritable in OBDA, even if the ontology is expressed in one of the most expressive members of the DL-Lite family
Computing CQ lower-bounds over OWL 2 through approximation to RSA
Conjunctive query (CQ) answering over knowledge bases is an important
reasoning task. However, with expressive ontology languages such as OWL, query
answering is computationally very expensive. The PAGOdA system addresses this
issue by using a tractable reasoner to compute lower and upper-bound
approximations, falling back to a fully-fledged OWL reasoner only when these
bounds don't coincide. The effectiveness of this approach critically depends on
the quality of the approximations, and in this paper we explore a technique for
computing closer approximations via RSA, an ontology language that subsumes all
the OWL 2 profiles while still maintaining tractability. We present a novel
approximation of OWL 2 ontologies into RSA, and an algorithm to compute a
closer (than PAGOdA) lower bound approximation using the RSA combined approach.
We have implemented these algorithms in a prototypical CQ answering system, and
we present a preliminary evaluation of our system that shows significant
performance improvements w.r.t. PAGOdA.Comment: 26 pages, 1 figur
Oblivious Bounds on the Probability of Boolean Functions
This paper develops upper and lower bounds for the probability of Boolean
functions by treating multiple occurrences of variables as independent and
assigning them new individual probabilities. We call this approach dissociation
and give an exact characterization of optimal oblivious bounds, i.e. when the
new probabilities are chosen independent of the probabilities of all other
variables. Our motivation comes from the weighted model counting problem (or,
equivalently, the problem of computing the probability of a Boolean function),
which is #P-hard in general. By performing several dissociations, one can
transform a Boolean formula whose probability is difficult to compute, into one
whose probability is easy to compute, and which is guaranteed to provide an
upper or lower bound on the probability of the original formula by choosing
appropriate probabilities for the dissociated variables. Our new bounds shed
light on the connection between previous relaxation-based and model-based
approximations and unify them as concrete choices in a larger design space. We
also show how our theory allows a standard relational database management
system (DBMS) to both upper and lower bound hard probabilistic queries in
guaranteed polynomial time.Comment: 34 pages, 14 figures, supersedes: http://arxiv.org/abs/1105.281
From Causes for Database Queries to Repairs and Model-Based Diagnosis and Back
In this work we establish and investigate connections between causes for
query answers in databases, database repairs wrt. denial constraints, and
consistency-based diagnosis. The first two are relatively new research areas in
databases, and the third one is an established subject in knowledge
representation. We show how to obtain database repairs from causes, and the
other way around. Causality problems are formulated as diagnosis problems, and
the diagnoses provide causes and their responsibilities. The vast body of
research on database repairs can be applied to the newer problems of computing
actual causes for query answers and their responsibilities. These connections,
which are interesting per se, allow us, after a transition -inspired by
consistency-based diagnosis- to computational problems on hitting sets and
vertex covers in hypergraphs, to obtain several new algorithmic and complexity
results for database causality.Comment: To appear in Theory of Computing Systems. By invitation to special
issue with extended papers from ICDT 2015 (paper arXiv:1412.4311
On the Complexity of Query Result Diversification
Query result diversification is a bi-criteria optimization problem for ranking query results. Given a database D, a query Q and a positive integer k, it is to find a set of k tuples from Q(D) such that the tuples are as relevant as possible to the query, and at the same time, as diverse as possible to each other. Subsets of Q(D) are ranked by an objective function defined in terms of relevance and diversity. Query result diversification has found a variety of applications in databases, information retrieval and operations research. This paper studies the complexity of result diversification for relational queries. We identify three problems in connection with query result diversification, to determine whether there exists a set of k tuples that is ranked above a bound with respect to relevance and diversity, to assess the rank of a given k-element set, and to count how many k-element sets are ranked above a given bound. We study these problems for a variety of query languages and for three objective functions. We establish the upper and lower bounds of these problems, all matching, for both combined complexity and data complexity. We also investigate several special settings of these problems, identifying tractable cases. 1
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