Revisiting the Notion of Extension over Incomplete Abstract Argumentation Frameworks

Bettina Fazzinga, Sergio Flesca, Filippo Furfaro

Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence

Main track. Pages 1712-1718.

Abstract

We revisit the notion of i-extension, i.e., the adaption of the fundamental

notion of extension to the case of incomplete Abstract

Argumentation Frameworks.

We show that the definition of i-extension raises some concerns in the

"possible" variant, e.g., it allows even conflicting arguments

to be collectively considered as members of an (i-)extension.

Thus, we introduce the alternative notion of i*-extension overcoming the

highlighted problems, and provide a thorough complexity characterization of the

corresponding verification problem.

Interestingly, we show that the revisitation not only has beneficial effects for

the semantics, but also for the complexity: under various semantics,

the verification problem under the possible perspective moves from NP-complete

to P.