Authors:
Van-Giang Trinh
1
;
Belaid Benhamou
2
and
Vincent Risch
2
Affiliations:
1
Inria Saclay, EP Lifeware, Palaiseau, France
;
2
LIRICA Team, LIS, Aix-Marseille University, Marseille, France
Keyword(s):
Abstract Argumentation Framework, Extension-Based Semantics, Graphical Analysis, Boolean Network.
Abstract:
Abstract Argumentation Frameworks (AFs) are the key formalism of abstract argumentation, which is one of the main directions in argumentation research. An AF is mainly studied by means of its extensions, defined as subsets of arguments. In this work, we define a Boolean Network (BN) encoding for AFs, where BNs are a simple and efficient mathematical formalism that has a long history of research. We then show that the attack graph of an AF coincides with the influence graph of its encoded BN, and in particular preferred and stable extensions of this AF one-to-one correspond to minimal trap spaces and fixed points of the encoded BN, respectively. We also define a new concept for BNs called complete trap space, then show that complete trap spaces (resp. the percolation of the special trap space where all variables are free) in BNs one-to-one correspond (resp. corresponds) to complete extensions (resp. the grounded extension) in AFs. This connection opens the promising application to gra
phical analysis of AFs, which is an interesting line of research with many useful applications. More specifically, we use it to explore many new results relating extensions of an AF and (positive or negative) cycles in its attack graph. In particular, we show new upper bounds based on positive feedback vertex sets for the numbers of stable, preferred, and complete extensions.
(More)