Semantic Web applications based on the Web Ontology Language (OWL) often
require the use of numbers in class descriptions for expressing
cardinality restrictions on properties or even classes. Some of these
cardinalities are specified explicitly, but quite a few are entailed and
need to be discovered by reasoning procedures. Due to the Description
Logic (DL) foundation of OWL, those reasoning services are offered by DL
reasoners. Existing DL reasoners employ reasoning procedures that are
arithmetically uninformed and substitute arithmetic reasoning by "don't
know" non-determinism in order to cover all possible cases. This lack of
information about arithmetic problems dramatically degrades the
performance of DL reasoners in many cases, especially with ontologies
relying on the use of Nominals and Qualied Cardinality Restrictions.
The contribution of this thesis is twofold: on the theoretical level, it
presents algebra�ic reasoning with DL (ReAl DL) using a sound, complete,
and terminating reasoning procedure for the DL SHOQ. ReAl DL combines
tableau reasoning procedures with algebraic methods, namely Integer
Programming, to ensure arithmetically better informed reasoning. SHOQ
extends the standard DL ALC with transitive roles, role hierarchies,
qualified cardinality restrictions (QCRs), and nominals, and forms an
expressive subset of OWL. Although the proposed algebraic tableau is
double exponential in the worst case, it deals with cardinalities with
an additional level of information and properties that make the calculus
amenable and well suited for optimizations. In order for ReAl DL to have
a practical merit, suited optimizations are proposed towards achieving
an efficient reasoning approach that addresses the sources of complexity
related to nominals and QCRs. On the practical level, a running
prototype reasoner (HARD) is implemented based on the proposed calculus
and optimizations. HARD is used to evaluate the practical merit of ReAl
DL, as well as the effectiveness of the proposed optimizations.
Experimental results based on real world and synthetic ontologies show
that ReAl DL outperforms existing reasoning approaches in handling the
interactions between nominals and QCRs. ReAl DL also comes with some
interesting features such as the ability to handle ontologies with
cyclic descriptions without adopting special blocking strategies. ReAl
DL can form a basis to provide more efficient reasoning support for
ontologies using nominals or QCRs
