Among the various proposals for defeasible reasoning for description
logics, Rational Closure, a procedure originally defined for propositional logic,
turns out to have a number of desirable properties. Not only it is computationally
feasible, but it can also be implemented using existing classical reasoners. One
of its drawbacks is that it can be seen as too weak from the inferential point of
view. To overcome this limitation we introduce in this paper two extensions of
Rational Closure: Basic Relevant Closure and Minimal Relevant Closure. As the
names suggest, both rely on defining a version of relevance. Our formalisation
of relevance in this context is based on the notion of a justification (a minimal
subset of sentences implying a given sentence). This is, to our knowledge, the
first proposal for defining defeasibility in terms of justifications—a notion that
is well-established in the area of ontology debugging. Both Basic and Minimal
Relevant Closure increase the inferential power of Rational Closure, giving back
intuitive conclusions that cannot be obtained from Rational Closure. We analyse
the properties and present algorithms for both Basic and Minimal Relevant
Closure, and provide experimental results for both Basic Relevant Closure and
Minimal Relevant Closure, comparing it with Rational Closure.
@{107,
author = {Giovanni Casini and Tommie Meyer and Kody Moodley and Riku Nortjé},
title = {Relevant Closure: A New Form of Defeasible Reasoning for Description Logics},
abstract = {Among the various proposals for defeasible reasoning for description
logics, Rational Closure, a procedure originally defined for propositional logic,
turns out to have a number of desirable properties. Not only it is computationally
feasible, but it can also be implemented using existing classical reasoners. One
of its drawbacks is that it can be seen as too weak from the inferential point of
view. To overcome this limitation we introduce in this paper two extensions of
Rational Closure: Basic Relevant Closure and Minimal Relevant Closure. As the
names suggest, both rely on defining a version of relevance. Our formalisation
of relevance in this context is based on the notion of a justification (a minimal
subset of sentences implying a given sentence). This is, to our knowledge, the
first proposal for defining defeasibility in terms of justifications—a notion that
is well-established in the area of ontology debugging. Both Basic and Minimal
Relevant Closure increase the inferential power of Rational Closure, giving back
intuitive conclusions that cannot be obtained from Rational Closure. We analyse
the properties and present algorithms for both Basic and Minimal Relevant
Closure, and provide experimental results for both Basic Relevant Closure and
Minimal Relevant Closure, comparing it with Rational Closure.},
year = {2014},
journal = {JELIA 2014},
pages = {92-106},
month = {24/09-26/09},
isbn = {978-3-319-11557-3},
}
