Connecting Abstract Argumentation Frameworks and Boolean Networks

Thời gian: 10h15-11h15 sáng Thứ 3, ngày 12/08/2025

Địa điểm: Phòng 507 nhà A6

Tóm tắt: 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. We use the connection 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. The established connection opens various directions of research in both areas.