Abstract Dialectical Frameworks are Boolean Networks (full version)

TL;DR

This paper explores the connection between Abstract Dialectical Frameworks and Boolean Networks, revealing similarities and differences to enhance understanding and enable new results in formal argumentation and biological modeling.

Contribution

It establishes a formal correspondence between dialectical frameworks and Boolean networks, bridging two distinct communities and enabling cross-disciplinary insights.

Findings

Revealed structural similarities between argumentation frameworks and biological networks.

Introduced a formal correspondence allowing transfer of results between the two formalisms.

Enabled new theoretical insights and potential applications across argumentation and biology.

Abstract

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.