Bridging abstract dialectical argumentation and Boolean gene regulation

TL;DR

This paper investigates structural parallels between abstract dialectical argumentation (ADFs and Dung frameworks) and Boolean gene networks (BNs). It treats both as bit-vector to bit-vector mappings and introduces a unified lens through which acceptance conditions and regulatory functions correspond to update operators; it reviews semantics, computation, and complexity, and shows how minimal trap spaces align with preferred interpretations. The work clarifies key differences, notably conflict-freedom, asynchrony, and derivative-based interactions, and proposes reconciliations via strict interaction notions and enriched influence graphs. It also discusses practical tools for computing admissible interpretations and trap spaces, benchmarks contrasting SAT/ASP-based methods, and outlines avenues for cross-fertilization, including abstraction, decomposition, counterfactual reasoning, and time-aware extensions. Overall, the contribution lays a foundation for transferring concepts and techniques between argumentation theory and gene-regulatory modeling to advance both fields.

Abstract

This paper leans on two similar areas so far detached from each other. On the one hand, Dung's pioneering contributions to abstract argumentation, almost thirty years ago, gave rise to a plethora of successors, including abstract dialectical frameworks (ADFs). On the other hand, Boolean networks (BNs), devised as models of gene regulation, have been successful for studying the behavior of molecular processes within cells. ADFs and BNs are similar to each other: both can be viewed as functions from vectors of bits to vectors of bits. As soon as similarities emerge between these two formalisms, however, differences appear. For example, conflict-freedom is prominent in argumentation (where we are interested in a self-consistent, i.e., conflict-free, set of beliefs) but absent in BNs. By contrast, asynchrony (where only one gene is updated at a time) is conspicuous in BNs and lacking in argumentation. Finally, while a monotonicity-based notion occurs in signed reasoning of both argumentation and gene regulation, a different, derivative-based notion only appears in the BN literature. To identify common mathematical structure between both formalisms, these differences need clarification. This contribution is a partial review of both these areas, where we cover enough ground to exhibit their more evident similarities, to then reconcile some of their apparent differences. We highlight a range of avenues of research resulting from ironing out discrepancies between these two fields. Unveiling their common concerns should enable these two areas to cross-fertilize so as to transfer ideas and results between each other.

Figures (9)

• Figure 1: Graphical representation of Example \ref{['ex-running']}.
• Figure 2: Example of a stable extension. All arguments in $X$ attack all arguments not in $X$.
• Figure 3: Example of an admissible set. All arguments in $X$ attack all arguments that attack $X$.
• Figure 4: Graphical representation of Example \ref{['ex-running']} (left) along with its two-valued update function $f_\mathcal{D}$ (right), where each arrow of the latter is an application of $f_\mathcal{D}$.
• Figure 5: The Caminada labeling resulting from applying $\mathcal{L}$ to the complete extension named $8$ of Figure \ref{['fig-running-state-transition-graph']}.

Theorems & Definitions (11)

• Example 1
• Lemma 1
• Lemma 2: caminada-06a
• Lemma 3: caminada-06a
• Lemma 4: brewka-woltran-10
• Lemma 5
• proof
• Theorem 1: klarner-14
• Corollary 1: klarner-14trinh-benhamou-soliman-23
• Theorem 2