Since OWL-K corresponds to S H O I N K (D)
DL, we have the following corollary.
Corollary 5.1 The OWL-K concept satisfiability
problem w.r.t a knowledge base is decidable.
According to Tobies (Tobies, 2001), if L is a
DL that provides the nominal constructor, knowledge
base satisfiability can be polynomially reduced to the
concept satisfiability w.r.t a knowledge base. So that
we obtain the following theorem.
Theorem 5.2 The knowledge base satisfiability prob-
lem of OWL-K is decidable.
6 DISCUSSION AND
PERSPECTIVES
We have proposed OWL-K as a decidable extension
of OWL-DL. This language supports ICs, which can-
not be represented in OWL-DL. The underpinning
DL of the latter,
S H O I N (D), is already known
with the complexity of NExpTime-complete (Tobies,
2000). Consequently, OWL-K has a difficult entail-
ment problem. The extension of the language pre-
sented here, therefore, are built like detachable com-
ponents for various needs.
Considering recent works adressing the same
problem, (Dou et al., 2006) introduced an ontology-
based framework, OntoGrate, using the web ontol-
ogy language Web-PDDL to incorporate database
schemas. This language allows IC representation.
However, it is written in RDF, an older formalism
with a lower capability than that of OWL. Even wrap-
ping one more layer translating Web-PDDL to OWL
syntax to facilitate worldwide use, the language is un-
decidable because its semantics is based on First Or-
der Logic (FOL), which is well known to be undecid-
able.
Some other works are discussed in (Chen et al.,
2006; Kalfoglou et al., 2005). However, to the best of
our knowledge, there exists no integrating framework
at the database schema level that provides a formal se-
mantic web ontology language, supporting OWL and
IC representation, and at the same time affording a
decidable reasoning procedure.
Our work comes within the perspective of a global
project to construct a methodology of integration of
relational data sources into the Semantic Web envi-
ronment. This integration will be realized through the
model ORM (Object Role Modeling) (Halpin, 2006).
The project consists of the study of the mapping with-
out loss of semantics of ORM schemas to a Web on-
tology language, i.e. OWL-K introduced here. Future
work will turn towards the research on the automated
translation of requests from OWL-K to SQL by using
the above mentioned mapping.
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