19,802 research outputs found
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
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
The Vadalog System: Datalog-based Reasoning for Knowledge Graphs
Over the past years, there has been a resurgence of Datalog-based systems in
the database community as well as in industry. In this context, it has been
recognized that to handle the complex knowl\-edge-based scenarios encountered
today, such as reasoning over large knowledge graphs, Datalog has to be
extended with features such as existential quantification. Yet, Datalog-based
reasoning in the presence of existential quantification is in general
undecidable. Many efforts have been made to define decidable fragments. Warded
Datalog+/- is a very promising one, as it captures PTIME complexity while
allowing ontological reasoning. Yet so far, no implementation of Warded
Datalog+/- was available. In this paper we present the Vadalog system, a
Datalog-based system for performing complex logic reasoning tasks, such as
those required in advanced knowledge graphs. The Vadalog system is Oxford's
contribution to the VADA research programme, a joint effort of the universities
of Oxford, Manchester and Edinburgh and around 20 industrial partners. As the
main contribution of this paper, we illustrate the first implementation of
Warded Datalog+/-, a high-performance Datalog+/- system utilizing an aggressive
termination control strategy. We also provide a comprehensive experimental
evaluation.Comment: Extended version of VLDB paper
<https://doi.org/10.14778/3213880.3213888
On the k-Boundedness for Existential Rules
The chase is a fundamental tool for existential rules. Several chase variants
are known, which differ on how they handle redundancies possibly caused by the
introduction of nulls. Given a chase variant, the halting problem takes as
input a set of existential rules and asks if this set of rules ensures the
termination of the chase for any factbase. It is well-known that this problem
is undecidable for all known chase variants. The related problem of boundedness
asks if a given set of existential rules is bounded, i.e., whether there is a
predefined upper bound on the number of (breadth-first) steps of the chase,
independently from any factbase. This problem is already undecidable in the
specific case of datalog rules. However, knowing that a set of rules is bounded
for some chase variant does not help much in practice if the bound is unknown.
Hence, in this paper, we investigate the decidability of the k-boundedness
problem, which asks whether a given set of rules is bounded by an integer k. We
prove that k-boundedness is decidable for three chase variants, namely the
oblivious, semi-oblivious and restricted chase.Comment: 20 pages, revised version of the paper published at RuleML+RR 201
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