4,114 research outputs found
Inclusion and Exclusion Dependencies in Team Semantics: On Some Logics of Imperfect Information
We introduce some new logics of imperfect information by adding atomic
formulas corresponding to inclusion and exclusion dependencies to the language
of first order logic. The properties of these logics and their relationships
with other logics of imperfect information are then studied. Furthermore, a
game theoretic semantics for these logics is developed. As a corollary of these
results, we characterize the expressive power of independence logic, thus
answering an open problem posed in (Gr\"adel and V\"a\"an\"anen, 2010)
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
Distribution Constraints: The Chase for Distributed Data
This paper introduces a declarative framework to specify and reason about distributions of data over computing nodes in a distributed setting. More specifically, it proposes distribution constraints which are tuple and equality generating dependencies (tgds and egds) extended with node variables ranging over computing nodes. In particular, they can express co-partitioning constraints and constraints about range-based data distributions by using comparison atoms. The main technical contribution is the study of the implication problem of distribution constraints. While implication is undecidable in general, relevant fragments of so-called data-full constraints are exhibited for which the corresponding implication problems are complete for EXPTIME, PSPACE and NP. These results yield bounds on deciding parallel-correctness for conjunctive queries in the presence of distribution constraints
Composition with Target Constraints
It is known that the composition of schema mappings, each specified by
source-to-target tgds (st-tgds), can be specified by a second-order tgd (SO
tgd). We consider the question of what happens when target constraints are
allowed. Specifically, we consider the question of specifying the composition
of standard schema mappings (those specified by st-tgds, target egds, and a
weakly acyclic set of target tgds). We show that SO tgds, even with the
assistance of arbitrary source constraints and target constraints, cannot
specify in general the composition of two standard schema mappings. Therefore,
we introduce source-to-target second-order dependencies (st-SO dependencies),
which are similar to SO tgds, but allow equations in the conclusion. We show
that st-SO dependencies (along with target egds and target tgds) are sufficient
to express the composition of every finite sequence of standard schema
mappings, and further, every st-SO dependency specifies such a composition. In
addition to this expressive power, we show that st-SO dependencies enjoy other
desirable properties. In particular, they have a polynomial-time chase that
generates a universal solution. This universal solution can be used to find the
certain answers to unions of conjunctive queries in polynomial time. It is easy
to show that the composition of an arbitrary number of standard schema mappings
is equivalent to the composition of only two standard schema mappings. We show
that surprisingly, the analogous result holds also for schema mappings
specified by just st-tgds (no target constraints). This is proven by showing
that every SO tgd is equivalent to an unnested SO tgd (one where there is no
nesting of function symbols). Similarly, we prove unnesting results for st-SO
dependencies, with the same types of consequences.Comment: This paper is an extended version of: M. Arenas, R. Fagin, and A.
Nash. Composition with Target Constraints. In 13th International Conference
on Database Theory (ICDT), pages 129-142, 201
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