In this paper we study formal properties of approaches to the reasoning with prioritized defeasible assumptions. We focus on methods proposed in formal argumentation, more specifically in the context of assumption- based argumentation.
We systematically compare two approaches for handling conflicts: pref- erence-based defeats and preference-based defeats extended with reverse defeat. We investigate under which conditions these approaches give rise to the same output. We study several meta-theoretical properties includ- ing argumentation theoretical properties (such as Dung’s Fundamental Lemma and the consistency of extensions) and properties for nonmono- tonic reasoning (such as Cautious Monotony and Cut) in a parametrized way, i.e., relative to specific constraints on the underlying deducability relation. Finally, we study the relationship between these approaches and preferred subtheories, a nonmonotonic reasoning formalism that is based on maximal consistent subsets of a totally ordered knowledge base.
In the parametrized setting we study different sub-classes of assumption- based argumentation frameworks. For instance, we identify a particularly well-behaved sub-class of argumentation-based frameworks for which the different conflict-handling mechanisms coincide, which give the same out- comes as preferred subtheories and for which core properties of nonmono- tonic logic are valid.
Keywords: structured argumentation; abstract argumentation; non- monotonic logic; defeasible reasoning; preferred subtheories; maximal consistent sets; preferences; priorities; 1 Introduction