Grounded Semantics and Principle-based Analysis for Incomplete Argumentation Frameworks

Abstract

Incomplete Argumentation Frameworks (IAFs) enrich classical abstract argumentation with arguments and attacks whose actual existence is questionable. The usual reasoning approaches rely on the notion of completion, i.e. standard AFs representing “possible worlds” compatible with the uncertain information encoded in the IAF. Recently, extension-based semantics for IAFs that do not rely on the notion of completion have been defined, using instead new versions of conflict-freeness and defense that take into account the (certain or uncertain) nature of arguments and attacks. In this paper, we give new insights on both the “completion-based” and the “direct” reasoning approaches. First, we adapt the well-known grounded semantics to this framework in two different versions that do not rely on completions. After determining that our new semantics are polynomially computable, we provide a principle-based analysis of these semantics, as well as the “direct” semantics previously defined in the literature, namely the complete, preferred and stable semantics. Finally, we also provide new results regarding the satisfaction of principles by the classical “completion-based” semantics.