Abstract
Abstract dialectical frameworks (ADFs) are generalizations of Dung’s argumentation frameworks which allow arbitrary relationships among arguments to be expressed. In particular, arguments can not only attack each other, they also may provide support for other arguments and interact in various complex ways. The ADF approach has recently been extended in two different ways. On the one hand, GRAPPA is a framework that applies the key notions underlying ADFs – in particular their operator-based semantics – directly to arbitrary labelled graphs. This allows users to represent argumentation scenarios in their favourite graphical representations without giving up the firm ground of well-defined semantics. On the other hand, ADFs have been further generalized to the multi-valued case to enable fine-grained acceptance values. In this paper we unify these approaches and develop a multi-valued version of GRAPPA combining the advantages of both extensions.
This research has been supported by DFG (Research Unit 1513 and project BR 1817/7-2) and FWF (project I2854).
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Notes
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- 2.
We call a parent \(n'\) of a node n l-parent if the link \((n',n)\) is labelled with l.
- 3.
We will often leave \(\varSigma \) implicit in definitions from now on.
- 4.
The values \(val^m(max_{W,\preccurlyeq }(l))\) and \(val^m(min_{W,\preccurlyeq }(l))\) are only defined when \(\hat{\preccurlyeq }\) is an order that has a maximal, respectively, minimal, element for every subset of V. The expressions \(max_{W,\preccurlyeq }(l)\) and \(min_{W,\preccurlyeq }(l)\) may only be used when this is the case.
- 5.
The use of \(min_{W}\) and \(max_{W}\) is restricted to settings where the label domain L is numeric.
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Brewka, G., Pührer, J., Woltran, S. (2019). Multi-valued GRAPPA. In: Calimeri, F., Leone, N., Manna, M. (eds) Logics in Artificial Intelligence. JELIA 2019. Lecture Notes in Computer Science(), vol 11468. Springer, Cham. https://doi.org/10.1007/978-3-030-19570-0_6
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