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Specificity and Context Dependent Preferences in Argumentation Systems

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Artificial Intelligence and Machine Learning (BNAIC/Benelearn 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1805))

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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. 1.

    Arguments for inconsistencies cover rebutting attacks.

  2. 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. 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. 4.

    We do not have the space to list all relevant arguments and attack relations implied by the example.

  5. 5.

    Note that we are not referring to undercutting arguments that we use to resolve conflicts/inconsistencies.

  6. 6.

    An extension is a maximal conflict-free set of defeasible rule in the approach of Dung and Son.

  7. 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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  • DOI: https://doi.org/10.1007/978-3-031-39144-6_8

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