Abstract Dialectical Frameworks are Boolean Networks (full version)
This work bridges two distinct fields—formal argumentation and biological modeling—by showing their mathematical equivalence, which is incremental but enables cross-disciplinary insights.
The paper establishes a formal correspondence between abstract dialectical frameworks (ADFs) and Boolean networks, revealing their similarities and differences, and uses this connection to derive new theoretical results for both formalisms.
Dialectical frameworks are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. Their generality allow them to cover a number of different approaches with varying forms of representing the argumentation structure. Boolean regulatory networks are used to model the dynamics of complex biological processes, taking into account the interactions of biological compounds, such as proteins or genes. These models have proven highly useful for comprehending such biological processes, allowing to reproduce known behaviour and testing new hypotheses and predictions in silico, for example in the context of new medical treatments. While both these approaches stem from entirely different communities, it turns out that there are striking similarities in their appearence. In this paper, we study the relation between these two formalisms revealing their communalities as well as their differences, and introducing a correspondence that allows to establish novel results for the individual formalisms.