Connecting Abstract Argumentation and Boolean Networks

Abstract

Already in Dung’s seminal paper introducing Abstract Argumentation Frameworks (AFs), several connections to seemingly unrelated reasoning formalisms have been illustrated. In this work, we continue this trend and establish a connection between abstract argumentation frameworks and boolean networks (BNs). BNs, in a nutshell, mimic simple binary-valued systems, where for each point in time, the value of each bit (component) depends only on the other components’ values of the previous point in time of the network. This formalism is widely used to formally analyze biological processes, where from simple rules complex behavior emerges. We show that stable extensions of an arbitrary AF correspond to single state attractors of its canonically corresponding BN, the complete extensions correspond to a distinctive 2-state attractor, and the admissible sets correspond to the seeds of the BN. We thereby lay the groundwork for a fruitful exchange of ideas between the two research areas.