  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.
