27 research outputs found
The data-exchange chase under the microscope
In this paper we take closer look at recent developments for the chase
procedure, and provide additional results. Our analysis allows us create a
taxonomy of the chase variations and the properties they satisfy. Two of the
most central problems regarding the chase is termination, and discovery of
restricted classes of sets of dependencies that guarantee termination of the
chase. The search for the restricted classes has been motivated by a fairly
recent result that shows that it is undecidable to determine whether the chase
with a given dependency set will terminate on a given instance. There is a
small dissonance here, since the quest has been for classes of sets of
dependencies guaranteeing termination of the chase on all instances, even
though the latter problem was not known to be undecidable. We resolve the
dissonance in this paper by showing that determining whether the chase with a
given set of dependencies terminates on all instances is coRE-complete. For the
hardness proof we use a reduction from word rewriting systems, thereby also
showing the close connection between the chase and word rewriting. The same
reduction also gives us the aforementioned instance-dependent RE-completeness
result as a byproduct. For one of the restricted classes guaranteeing
termination on all instances, the stratified sets dependencies, we provide new
complexity results for the problem of testing whether a given set of
dependencies belongs to it. These results rectify some previous claims that
have occurred in the literature.Comment: arXiv admin note: substantial text overlap with arXiv:1303.668
All-Instances Restricted Chase Termination
The chase procedure is a fundamental algorithmic tool in database theory with
a variety of applications. A key problem concerning the chase procedure is
all-instances termination: for a given set of tuple-generating dependencies
(TGDs), is it the case that the chase terminates for every input database? In
view of the fact that this problem is undecidable, it is natural to ask whether
known well-behaved classes of TGDs ensure decidability. We consider here the
main paradigms that led to robust TGD-based formalisms, that is, guardedness
and stickiness. Although all-instances termination is well-understood for the
oblivious version of the chase, the more subtle case of the restricted (a.k.a.
the standard) chase is rather unexplored. We show that all-instances restricted
chase termination for guarded and sticky single-head TGDs is decidable
Oblivious Chase Termination:The Sticky Case
The chase procedure is one of the most fundamental algorithmic tools in database theory. A key algorithmic task is uniform chase termination, i.e., given a set of tuple-generating dependencies (tgds), is it the case that the chase under this set of tgds terminates, for every input database? In view of the fact that this problem is undecidable, no matter which version of the chase we consider, it is natural to ask whether well-behaved classes of tgds, introduced in different contexts such as ontological reasoning, make our problem decidable. In this work, we consider a prominent decidability paradigm for tgds, called stickiness. We show that for sticky sets of tgds, uniform chase termination is decidable if we focus on the (semi-)oblivious chase, and we pinpoint its exact complexity: PSpace-complete in general, and NLogSpace-complete for predicates of bounded arity. These complexity results are obtained via graph-based syntactic characterizations of chase termination that are of independent interest
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
Query Rewriting and Optimization for Ontological Databases
Ontological queries are evaluated against a knowledge base consisting of an
extensional database and an ontology (i.e., a set of logical assertions and
constraints which derive new intensional knowledge from the extensional
database), rather than directly on the extensional database. The evaluation and
optimization of such queries is an intriguing new problem for database
research. In this paper, we discuss two important aspects of this problem:
query rewriting and query optimization. Query rewriting consists of the
compilation of an ontological query into an equivalent first-order query
against the underlying extensional database. We present a novel query rewriting
algorithm for rather general types of ontological constraints which is
well-suited for practical implementations. In particular, we show how a
conjunctive query against a knowledge base, expressed using linear and sticky
existential rules, that is, members of the recently introduced Datalog+/-
family of ontology languages, can be compiled into a union of conjunctive
queries (UCQ) against the underlying database. Ontological query optimization,
in this context, attempts to improve this rewriting process so to produce
possibly small and cost-effective UCQ rewritings for an input query.Comment: arXiv admin note: text overlap with arXiv:1312.5914 by other author