Ordering Argumentation Frameworks

Chiaki Sakama and Katsumi Inoue

in: Proceedings of the 15th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2019), Lecture Notes in Artificial Intelligence 11726, pages 87-98, Springer-Verlag, 2019.

Abstract

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 ≤ _σ^b 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 ≤ _σ^b 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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