Ordering Argumentation Frameworks
Chiaki Sakama and Katsumi Inoue
Proceedings of the
15th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Lecture Notes in Artificial Intelligence 11726, pages 87-98, Springer-Verlag, 2019.
This paper introduces two orderings over abstract argumentation frameworks to compare justification
status under argumentation semantics.
Given two argumentation frameworks AF1 and AF2 and an argumentation semantics σ,
AF2 is more #-general than (or equal to) AF1
(written AF1 ≤ σ# AF2)
if for any σ-extension F of AF2 there is a σ-extension E of AF1 such that E⊆ F.
In contrast, AF2 is more b-general than (or equal to) AF1
(written AF1 ≤ σb AF2) if
for any σ-extension E of AF1 there is a σ-extension F of AF2 such that E⊆ F.
We show that if AF1 ≤ σ# AF2
then AF2 skeptically accepts arguments more than AF1 (under the σ-semantics)
while if AF1 ≤ σb AF2
then AF2 credulously accepts arguments more than AF1.
Mathematically, these orders constitute pre-order sets over the set of all argumentation frameworks.
Next we consider comparing two AFs under dynamic environments by observing the effect of
incorporating new information into given AFs. We introduce two orderings in such dynamic
environments and show its connection to strong equivalence between argumentation frameworks.
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