Abstract

Abstract Dialectical Frameworks (adfs) are generalizations of Dung's abstract argumentation frameworks (afs) where each argument has an associated acceptance condition expressed by a boolean formula. The resulting extension is robust enough not only to model the attack relation original to afs, but also others types of dependencies and interactions between arguments. A recent development in adfs proposed an alternative formalization involving three-valued acceptance conditions, connecting the original definitions of adfs to the concept of three-valued argument labellings, a core concept in computational argumentation literature. In this paper, we revise some of the main semantics defined under this three-valued approach and prove our definitions hold equivalence to well-known semantics of afs.

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