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Abstract
We give an introductory tutorial to assumption-based argumentation (referred to as ABA) – a form of argumentation where arguments and attacks are notions derived from primitive notions of rules in a deductive system, assumptions and contraries thereof. ABA is equipped with different semantics for determining ‘winning’ sets of assumptions and – interchangeably and equivalently – ‘winning’ sets of arguments. It is also equipped with a catalogue of computational techniques to determine whether given conclusions can be supported by a ‘winning’ set of arguments. These are in the form of disputes between (fictional) proponent and opponent players, provably correct w.r.t. the semantics. Albeit simple, ABA is powerful in that it can be used to represent and reason with a number of problems in AI and beyond: non-monotonic reasoning, preferences, decisions. While doing so, it encompasses the expressive and computational needs of these problems while affording the transparency and explanatory power of argumentation.
Acknowledgements
I am grateful to several colleagues for useful feedback and suggestions on earlier versions of this paper, and in particular to Tony Hunter, Claudia Schultz, Tony Kakas, Henry Prakken, Xiuyi Fan, Phan Minh Dung, and Bob Kowalski.
Notes
1. represents ‘true’ and stands for the empty body of rules. In other words, each rule
can be interpreted as
for the purpose of presenting deductions as trees.
2. We use here the following notions, for sets of arguments A, A′ and arguments α, α′:
(i) A attacks A′ iff there exist
and
(ii) α attacks A′ iff {α} attacks A′;
(iii) A attacks α′ iff A attacks {α′}.
3. A set S is maximally (w.r.t. ⊆) fulfilling property p iff there is no S′ ⊃ S such that S′ fulfils property p.
4. A set S is minimally (w.r.t. ⊆) fulfilling property p iff there is no S′⊂S such that S′ fulfils property p.
5. In the context of the realistic reading of the ABA framework in Example 3.1, here d may stand for ‘sad’.
6. The arguments in ,
are not explicit in the dispute derivations of Dung et al. (Citation2006, Citation2007) and are instead flattened out to a set of sentences (in
) and sets of sets of sentences (in
). We focus our discussion here on the dispute derivations of Toni (Citation2013).
7. The derivation is the same for both semantics, as the bits of the algorithm in bold make no difference in this example, as we will see.
8. The flowchart focuses on changes to the ,
, D and C components only and ignores changes to the dialectical structure – for simplicity and compactness of presentation.
9. www.doc.ic.ac.uk/ft/CaSAPI/, no longer maintained.