  Probabilistic epistemic argumentation allows for reasoning about
argumentation problems in a way that is well founded by probability theory.
Epistemic states are represented by probability functions over possible worlds
and can be adjusted to new beliefs using update operators. While the use of
probability functions puts this approach on a solid foundational basis, it also
causes computational challenges as the amount of data to process depends
exponentially on the number of arguments. This leads to bottlenecks in
applications such as modelling opponent's beliefs for persuasion dialogues. We
show how update operators over probability functions can be related to update
operators over much more compact representations that allow polynomial-time
updates. We discuss the cognitive and probabilistic-logical plausibility of
this approach and demonstrate its applicability in computational persuasion.
