6,306 research outputs found
Inductive Logic Programming in Databases: from Datalog to DL+log
In this paper we address an issue that has been brought to the attention of
the database community with the advent of the Semantic Web, i.e. the issue of
how ontologies (and semantics conveyed by them) can help solving typical
database problems, through a better understanding of KR aspects related to
databases. In particular, we investigate this issue from the ILP perspective by
considering two database problems, (i) the definition of views and (ii) the
definition of constraints, for a database whose schema is represented also by
means of an ontology. Both can be reformulated as ILP problems and can benefit
from the expressive and deductive power of the KR framework DL+log. We
illustrate the application scenarios by means of examples. Keywords: Inductive
Logic Programming, Relational Databases, Ontologies, Description Logics, Hybrid
Knowledge Representation and Reasoning Systems. Note: To appear in Theory and
Practice of Logic Programming (TPLP).Comment: 30 pages, 3 figures, 2 tables
Graphs of gonality three
In 2013, Chan classified all metric hyperelliptic graphs, proving that
divisorial gonality and geometric gonality are equivalent in the hyperelliptic
case. We show that such a classification extends to combinatorial graphs of
divisorial gonality three, under certain edge- and vertex-connectivity
assumptions. We also give a construction for graphs of divisorial gonality
three, and provide conditions for determining when a graph is not of divisorial
gonality three.Comment: 19 pages, 13 figures; corrected statements of Theorems 1.2 and 4.1,
as well as material in Section
Learning high-dimensional directed acyclic graphs with latent and selection variables
We consider the problem of learning causal information between random
variables in directed acyclic graphs (DAGs) when allowing arbitrarily many
latent and selection variables. The FCI (Fast Causal Inference) algorithm has
been explicitly designed to infer conditional independence and causal
information in such settings. However, FCI is computationally infeasible for
large graphs. We therefore propose the new RFCI algorithm, which is much faster
than FCI. In some situations the output of RFCI is slightly less informative,
in particular with respect to conditional independence information. However, we
prove that any causal information in the output of RFCI is correct in the
asymptotic limit. We also define a class of graphs on which the outputs of FCI
and RFCI are identical. We prove consistency of FCI and RFCI in sparse
high-dimensional settings, and demonstrate in simulations that the estimation
performances of the algorithms are very similar. All software is implemented in
the R-package pcalg.Comment: Published in at http://dx.doi.org/10.1214/11-AOS940 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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