9,274 research outputs found
Finite Open-World Query Answering with Number Restrictions (Extended Version)
Open-world query answering is the problem of deciding, given a set of facts,
conjunction of constraints, and query, whether the facts and constraints imply
the query. This amounts to reasoning over all instances that include the facts
and satisfy the constraints. We study finite open-world query answering (FQA),
which assumes that the underlying world is finite and thus only considers the
finite completions of the instance. The major known decidable cases of FQA
derive from the following: the guarded fragment of first-order logic, which can
express referential constraints (data in one place points to data in another)
but cannot express number restrictions such as functional dependencies; and the
guarded fragment with number restrictions but on a signature of arity only two.
In this paper, we give the first decidability results for FQA that combine both
referential constraints and number restrictions for arbitrary signatures: we
show that, for unary inclusion dependencies and functional dependencies, the
finiteness assumption of FQA can be lifted up to taking the finite implication
closure of the dependencies. Our result relies on new techniques to construct
finite universal models of such constraints, for any bound on the maximal query
size.Comment: 59 pages. To appear in LICS 2015. Extended version including proof
Finite Open-World Query Answering with Number Restrictions
Open-world query answering is the problem of deciding, given a set of facts,
conjunction of constraints, and query, whether the facts and constraints imply
the query. This amounts to reasoning over all instances that include the facts
and satisfy the constraints. We study finite open-world query answering (FQA),
which assumes that the underlying world is finite and thus only considers the
finite completions of the instance. The major known decidable cases of FQA
derive from the following: the guarded fragment of first-order logic, which can
express referential constraints (data in one place points to data in another)
but cannot express number restrictions such as functional dependencies; and the
guarded fragment with number restrictions but on a signature of arity only two.
In this paper, we give the first decidability results for FQA that combine both
referential constraints and number restrictions for arbitrary signatures: we
show that, for unary inclusion dependencies and functional dependencies, the
finiteness assumption of FQA can be lifted up to taking the finite implication
closure of the dependencies. Our result relies on new techniques to construct
finite universal models of such constraints, for any bound on the maximal query
size.Comment: 70 pages. Extended journal version of arXiv:1505.04216. This article
is the same as what will be published in ToCL, except for publisher-induced
changes, minor changes, and reordering of the material (in the ToCL version
some detailed proofs are moved from the article body to an appendix
Queries with Guarded Negation (full version)
A well-established and fundamental insight in database theory is that
negation (also known as complementation) tends to make queries difficult to
process and difficult to reason about. Many basic problems are decidable and
admit practical algorithms in the case of unions of conjunctive queries, but
become difficult or even undecidable when queries are allowed to contain
negation. Inspired by recent results in finite model theory, we consider a
restricted form of negation, guarded negation. We introduce a fragment of SQL,
called GN-SQL, as well as a fragment of Datalog with stratified negation,
called GN-Datalog, that allow only guarded negation, and we show that these
query languages are computationally well behaved, in terms of testing query
containment, query evaluation, open-world query answering, and boundedness.
GN-SQL and GN-Datalog subsume a number of well known query languages and
constraint languages, such as unions of conjunctive queries, monadic Datalog,
and frontier-guarded tgds. In addition, an analysis of standard benchmark
workloads shows that most usage of negation in SQL in practice is guarded
negation
Querying the Guarded Fragment
Evaluating a Boolean conjunctive query Q against a guarded first-order theory
F is equivalent to checking whether "F and not Q" is unsatisfiable. This
problem is relevant to the areas of database theory and description logic.
Since Q may not be guarded, well known results about the decidability,
complexity, and finite-model property of the guarded fragment do not obviously
carry over to conjunctive query answering over guarded theories, and had been
left open in general. By investigating finite guarded bisimilar covers of
hypergraphs and relational structures, and by substantially generalising
Rosati's finite chase, we prove for guarded theories F and (unions of)
conjunctive queries Q that (i) Q is true in each model of F iff Q is true in
each finite model of F and (ii) determining whether F implies Q is
2EXPTIME-complete. We further show the following results: (iii) the existence
of polynomial-size conformal covers of arbitrary hypergraphs; (iv) a new proof
of the finite model property of the clique-guarded fragment; (v) the small
model property of the guarded fragment with optimal bounds; (vi) a
polynomial-time solution to the canonisation problem modulo guarded
bisimulation, which yields (vii) a capturing result for guarded bisimulation
invariant PTIME.Comment: This is an improved and extended version of the paper of the same
title presented at LICS 201
Composition and Inversion of Schema Mappings
In the recent years, a lot of attention has been paid to the development of
solid foundations for the composition and inversion of schema mappings. In this
paper, we review the proposals for the semantics of these crucial operators.
For each of these proposals, we concentrate on the three following problems:
the definition of the semantics of the operator, the language needed to express
the operator, and the algorithmic issues associated to the problem of computing
the operator. It should be pointed out that we primarily consider the
formalization of schema mappings introduced in the work on data exchange. In
particular, when studying the problem of computing the composition and inverse
of a schema mapping, we will be mostly interested in computing these operators
for mappings specified by source-to-target tuple-generating dependencies
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