783 research outputs found
Discovering Implicational Knowledge in Wikidata
Knowledge graphs have recently become the state-of-the-art tool for
representing the diverse and complex knowledge of the world. Examples include
the proprietary knowledge graphs of companies such as Google, Facebook, IBM, or
Microsoft, but also freely available ones such as YAGO, DBpedia, and Wikidata.
A distinguishing feature of Wikidata is that the knowledge is collaboratively
edited and curated. While this greatly enhances the scope of Wikidata, it also
makes it impossible for a single individual to grasp complex connections
between properties or understand the global impact of edits in the graph. We
apply Formal Concept Analysis to efficiently identify comprehensible
implications that are implicitly present in the data. Although the complex
structure of data modelling in Wikidata is not amenable to a direct approach,
we overcome this limitation by extracting contextual representations of parts
of Wikidata in a systematic fashion. We demonstrate the practical feasibility
of our approach through several experiments and show that the results may lead
to the discovery of interesting implicational knowledge. Besides providing a
method for obtaining large real-world data sets for FCA, we sketch potential
applications in offering semantic assistance for editing and curating Wikidata
Linear Datalog and Bounded Path Duality of Relational Structures
In this paper we systematically investigate the connections between logics
with a finite number of variables, structures of bounded pathwidth, and linear
Datalog Programs. We prove that, in the context of Constraint Satisfaction
Problems, all these concepts correspond to different mathematical embodiments
of a unique robust notion that we call bounded path duality. We also study the
computational complexity implications of the notion of bounded path duality. We
show that every constraint satisfaction problem \csp(\best) with bounded path
duality is solvable in NL and that this notion explains in a uniform way all
families of CSPs known to be in NL. Finally, we use the results developed in
the paper to identify new problems in NL
On implicational bases of closure systems with unique critical sets
We show that every optimum basis of a finite closure system, in D.Maier's
sense, is also right-side optimum, which is a parameter of a minimum CNF
representation of a Horn Boolean function. New parameters for the size of the
binary part are also established. We introduce a K-basis of a general closure
system, which is a refinement of the canonical basis of Duquenne and Guigues,
and discuss a polynomial algorithm to obtain it. We study closure systems with
the unique criticals and some of its subclasses, where the K-basis is unique. A
further refinement in the form of the E-basis is possible for closure systems
without D-cycles. There is a polynomial algorithm to recognize the D-relation
from a K-basis. Thus, closure systems without D-cycles can be effectively
recognized. While E-basis achieves an optimum in one of its parts, the
optimization of the others is an NP-complete problem.Comment: Presented on International Symposium of Artificial Intelligence and
Mathematics (ISAIM-2012), Ft. Lauderdale, FL, USA Results are included into
plenary talk on conference Universal Algebra and Lattice Theory, June 2012,
Szeged, Hungary 29 pages and 2 figure
Attribute Exploration of Discrete Temporal Transitions
Discrete temporal transitions occur in a variety of domains, but this work is
mainly motivated by applications in molecular biology: explaining and analyzing
observed transcriptome and proteome time series by literature and database
knowledge. The starting point of a formal concept analysis model is presented.
The objects of a formal context are states of the interesting entities, and the
attributes are the variable properties defining the current state (e.g.
observed presence or absence of proteins). Temporal transitions assign a
relation to the objects, defined by deterministic or non-deterministic
transition rules between sets of pre- and postconditions. This relation can be
generalized to its transitive closure, i.e. states are related if one results
from the other by a transition sequence of arbitrary length. The focus of the
work is the adaptation of the attribute exploration algorithm to such a
relational context, so that questions concerning temporal dependencies can be
asked during the exploration process and be answered from the computed stem
base. Results are given for the abstract example of a game and a small gene
regulatory network relevant to a biomedical question.Comment: Only the email address and reference have been replace
Learning Description Logic Ontologies: Five Approaches. Where Do They Stand?
Abstract
The quest for acquiring a formal representation of the knowledge of a domain of interest has attracted researchers with various backgrounds into a diverse field called ontology learning. We highlight classical machine learning and data mining approaches that have been proposed for (semi-)automating the creation of description logic (DL) ontologies. These are based on association rule mining, formal concept analysis, inductive logic programming, computational learning theory, and neural networks. We provide an overview of each approach and how it has been adapted for dealing with DL ontologies. Finally, we discuss the benefits and limitations of each of them for learning DL ontologies
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