5 research outputs found
A logic programming framework for possibilistic argumentation: formalization and logical properties
In the last decade defeasible argumentation frameworks have evolved to become
a sound setting to formalize commonsense, qualitative reasoning. The logic programming
paradigm has shown to be particularly useful for developing different
argument-based frameworks on the basis of different variants of logic programming
which incorporate defeasible rules. Most of such frameworks, however, are unable to
deal with explicit uncertainty, nor with vague knowledge, as defeasibility is directly
encoded in the object language. This paper presents Possibilistic Logic Programming
(P-DeLP), a new logic programming language which combines features from
argumentation theory and logic programming, incorporating as well the treatment
of possibilistic uncertainty. Such features are formalized on the basis of PGL, a
possibilistic logic based on G¨odel fuzzy logic. One of the applications of P-DeLP
is providing an intelligent agent with non-monotonic, argumentative inference capabilities.
In this paper we also provide a better understanding of such capabilities
by defining two non-monotonic operators which model the expansion of a given
program P by adding new weighed facts associated with argument conclusions and
warranted literals, respectively. Different logical properties for the proposed operators
are studie
Interdefinability of defeasible logic and logic programming under the well-founded semantics
We provide a method of translating theories of Nute's defeasible logic into
logic programs, and a corresponding translation in the opposite direction.
Under certain natural restrictions, the conclusions of defeasible theories
under the ambiguity propagating defeasible logic ADL correspond to those of the
well-founded semantics for normal logic programs, and so it turns out that the
two formalisms are closely related. Using the same translation of logic
programs into defeasible theories, the semantics for the ambiguity blocking
defeasible logic NDL can be seen as indirectly providing an ambiguity blocking
semantics for logic programs. We also provide antimonotone operators for both
ADL and NDL, each based on the Gelfond-Lifschitz (GL) operator for logic
programs. For defeasible theories without defeaters or priorities on rules, the
operator for ADL corresponds to the GL operator and so can be seen as partially
capturing the consequences according to ADL. Similarly, the operator for NDL
captures the consequences according to NDL, though in this case no restrictions
on theories apply. Both operators can be used to define stable model semantics
for defeasible theories.Comment: 36 pages; To appear in Theory and Practice of Logic Programming
(TPLP