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G. Brewka, St. Ellmauthaler, H. Strass, J. P. Wallner, S. Woltran:
"Abstract Dialectical Frameworks";
in: "Handbook of Formal Argumentation", P. Baroni, D.M. Gabbay, M. Giacomin, L. van der Torre (Hrg.); College Publications, http://www.collegepublications.co.uk/handbooks/, 2018, ISBN: 978-1-84890-275-6, S. 237 - 285.

This handbook chapter describes abstract dialectical frameworks, or ADFs for short. ADFs are generalizations of the widely used Dung argumentation frameworks. Whereas the latter focus on a single relation among abstract arguments, namely attack, ADFs allow arbitrary relationships among arguments to be expressed. For instance, arguments may support each other, or a group of arguments may jointly attack another one while each single member of the group is not strong enough to do so. This additional expressiveness is achieved by handling acceptance conditions for each argument explicitly.
The semantics of ADFs are inspired by approximation fixpoint theory (AFT),
a general algebraic theory for approximation based semantics developed by
Denecker, Marek and Truszczyński. We briefly introduce AFT and discuss its
role in argumentation. This puts us in a position to formally introduce ADFs
and their semantics. In particular, we show how the most important Dung
semantics can be generalized to ADFs. Furthermore, we illustrate the use
of ADFs as semantical tool in various modelling scenarios, demonstrating how
typical representations in argumentation can be equipped with precise semantics
via translations to ADFs. We also present GRAPPA, a related approach where the
semantics of arbitrary labelled argument graphs can be directly defined in an
ADF-like manner, circumventing the need for explicit translations. Finally, we
address various computational aspects of ADFs, like complexity, expressiveness
and realizability, and present several implemented systems.

Projektleitung Johannes Peter Wallner:
EMBArg

Projektleitung Stefan Woltran:
Neue Werkzeuge für graphenbasierte formale Argumentation

Projektleitung Stefan Woltran:
Wissensadaption in Logik-Fragmenten