1,870 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
Using linear constraints for logic program termination analysis
It is widely acknowledged that function symbols are an important feature in
answer set programming, as they make modeling easier, increase the expressive
power, and allow us to deal with infinite domains. The main issue with their
introduction is that the evaluation of a program might not terminate and
checking whether it terminates or not is undecidable. To cope with this
problem, several classes of logic programs have been proposed where the use of
function symbols is restricted but the program evaluation termination is
guaranteed. Despite the significant body of work in this area, current
approaches do not include many simple practical programs whose evaluation
terminates. In this paper, we present the novel classes of rule-bounded and
cycle-bounded programs, which overcome different limitations of current
approaches by performing a more global analysis of how terms are propagated
from the body to the head of rules. Results on the correctness, the complexity,
and the expressivity of the proposed approach are provided.Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
Existential Rule Languages with Finite Chase: Complexity and Expressiveness
Finite chase, or alternatively chase termination, is an important condition
to ensure the decidability of existential rule languages. In the past few
years, a number of rule languages with finite chase have been studied. In this
work, we propose a novel approach for classifying the rule languages with
finite chase. Using this approach, a family of decidable rule languages, which
extend the existing languages with the finite chase property, are naturally
defined. We then study the complexity of these languages. Although all of them
are tractable for data complexity, we show that their combined complexity can
be arbitrarily high. Furthermore, we prove that all the rule languages with
finite chase that extend the weakly acyclic language are of the same
expressiveness as the weakly acyclic one, while rule languages with higher
combined complexity are in general more succinct than those with lower combined
complexity.Comment: Extended version of a paper to appear on AAAI 201
ChaTEAU: A Universal Toolkit for Applying the Chase
What do applications like semantic optimization, data exchange and integration, answering queries under dependencies, query reformulation with constraints, and data cleaning have in common? All these applications can be processed by the Chase, a family of algorithms for reasoning with constraints. While the theory of the Chase is well understood, existing implementations are confined to specific use cases and application scenarios, making it difficult to reuse them in other settings. ChaTEAU overcomes this limitation: It takes the logical core of the Chase, generalizes it, and provides a software library for different Chase applications in a single toolkit
- …