Practical reasoning for defeasable description logics.
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Date
2016
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Abstract
Description Logics (DLs) are a family of logic-based languages for formalising
ontologies. They have useful computational properties allowing the development
of automated reasoning engines to infer implicit knowledge from
ontologies. However, classical DLs do not tolerate exceptions to speci ed
knowledge. This led to the prominent research area of nonmonotonic or defeasible
reasoning for DLs, where most techniques were adapted from seminal
works for propositional and rst-order logic.
Despite the topic's attention in the literature, there remains no consensus
on what \sensible" defeasible reasoning means for DLs. Furthermore, there
are solid foundations for several approaches and yet no serious implementations
and practical tools. In this thesis we address the aforementioned issues
in a broad sense. We identify the preferential approach, by Kraus, Lehmann
and Magidor (KLM) in propositional logic, as a suitable abstract framework
for de ning and studying the precepts of sensible defeasible reasoning.
We give a generalisation of KLM's precepts, and their arguments motivating
them, to the DL case. We also provide several preferential algorithms
for defeasible entailment in DLs; evaluate these algorithms, and the main
alternatives in the literature, against the agreed upon precepts; extensively
test the performance of these algorithms; and ultimately consolidate our implementation
in a software tool called Defeasible-Inference Platform (DIP).
We found some useful entailment regimes within the preferential context
that satisfy all the KLM properties, and some that have scalable performance
in real world ontologies even without extensive optimisation.
Description
Doctor of Philosophy in Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Durban 2016.
Keywords
Theses - Mathematics and Computer Science Education.