Abstract
Dung and Son [6] argue that specificity as a criterion for resolving conflicts between arguments, is context dependent. They propose to use arguments to address the context dependency of specificity in combination with a new special argumentation semantics. Unfortunately, their solution is restricted to argumentation systems without undercutting arguments. This paper presents a more general solution which allows for undercutting arguments and allows for any argumentation semantics. Moreover, the solution is applicable to any form a context dependent preferences.
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Notes
- 1.
Arguments for inconsistencies cover rebutting attacks.
- 2.
Note the difference between an undercutting argument and an undercutting defeater. The former is an argument for not using a proposition or a defeasible rule, and the latter is a defeasible rule specifying a condition under which another defeasible rule should not be used [12].
- 3.
In argument A we use the symbol \(|\circ \) to indicate that the preference \(\eta \leadsto \mu < \varphi \leadsto \psi \) does not deductively follow from \(\eta \) in the support: \(\mathcal {S} = [\alpha \vdash \alpha \leadsto \varphi \vdash \varphi \leadsto \eta ]\).
- 4.
We do not have the space to list all relevant arguments and attack relations implied by the example.
- 5.
Note that we are not referring to undercutting arguments that we use to resolve conflicts/inconsistencies.
- 6.
An extension is a maximal conflict-free set of defeasible rule in the approach of Dung and Son.
- 7.
In the original version of the argumentation system used in this paper [18, 19], a stable extension was defined as the fixed point of a function \( DR(\mathcal {X}) = \{\varphi \leadsto \psi \mid A\in \mathcal {A}, \mathcal {X} \cap \tilde{A} = \varnothing , \hat{A}={\textbf {not}}(\varphi \leadsto \psi ) \} \) returning a set of defeated rules if \(\mathcal {X}\) is a set of defeated rules. \(\mathcal {A-X}\) is a maximal set of default rules given the definition of an extension used by Dung and Son [6].
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Roos, N. (2023). Specificity and Context Dependent Preferences in Argumentation Systems. In: Calders, T., Vens, C., Lijffijt, J., Goethals, B. (eds) Artificial Intelligence and Machine Learning. BNAIC/Benelearn 2022. Communications in Computer and Information Science, vol 1805. Springer, Cham. https://doi.org/10.1007/978-3-031-39144-6_8
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