Abstract
It has been shown that entailments based on the maximally consistent subsets (MCS) of a given set of premises can be captured by Dung-style semantics for argumentation frameworks. This paper shows that these links are much tighter and go way beyond simplified forms of reasoning with MCS. Among others, we consider different types of entailments that these kinds of reasoning induce, extend the framework for arbitrary (not necessarily maximal) consistent subsets, and incorporate non-classical logics. The introduction of declarative methods for reasoning with MCS by means of (sequent-based) argumentation frameworks provides, in particular, a better understanding of logic-based argumentation and allows to reevaluate some negative results concerning the latter.
O. Arieli and A. Borg—Supported by the Israel Science Foundation (grant 817/15).
A. Borg and C. Straßer—Supported by the Alexander von Humboldt Foundation and the German Ministry for Education and Research.
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Notes
- 1.
Thus, unlike \(\varGamma \), \(\varDelta \), when \(\mathsf{S}\), \(\mathsf{T}\) are assumed to be finite, this will be indicated explicitly.
- 2.
Somewhat abusing the notations, we shall sometimes identify \( Attack \) with \({\mathfrak A}\).
- 3.
To prevent attacks on tautologies, in Defeating Rebuttal we assume that \(\varGamma _2 \ne \emptyset \).
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Arieli, O., Borg, A., Straßer, C. (2017). Argumentative Approaches to Reasoning with Consistent Subsets of Premises. In: Benferhat, S., Tabia, K., Ali, M. (eds) Advances in Artificial Intelligence: From Theory to Practice. IEA/AIE 2017. Lecture Notes in Computer Science(), vol 10350. Springer, Cham. https://doi.org/10.1007/978-3-319-60042-0_50
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