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Constrained Incomplete Argumentation Frameworks

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12897))

Abstract

Operations like belief change or merging have been adapted to the context of abstract argumentation. However, these operations may require to express some uncertainty or some disjunction in the result, which is not representable in classical AFs. For this reason, some of these works require a set of AFs or a set of extensions as the outcome of the operation, somehow to represent a disjunction of AFs or extensions. In parallel, the notion of Incomplete AFs (IAFs) has been developed recently. It corresponds to AFs where the existence of some arguments or attacks may be uncertain. Each IAF can be associated with a set of classical AFs called completions, that correspond to different ways of “resolving the uncertainty”. While these IAFs could be good candidates for a compact representation of a “disjunction” of AFs, we prove that this model is not expressive enough. Then we introduce Constrained IAFs, that include a propositional formula allowing to select the set of completions used for reasoning. We prove that this model is expressive enough for representing any set of AFs, or any set of extensions. Moreover, we show that the complexity of credulous and skeptical reasoning is the same as in the case of IAFs. Finally, we show that CIAFs can be used to model a new form of extension enforcement.

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Notes

  1. 1.

    Proofs are omitted for space reasons.

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Acknowledgements

The author warmly thanks Antonio Yuste-Ginel for the interesting discussion that lead to this work, as well as the reviewers that provided valuable feedback.

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Authors and Affiliations

  1. LIPADE, University of Paris, Paris, France

    Jean-Guy Mailly

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  1. Jean-Guy Mailly
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Correspondence to Jean-Guy Mailly .

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  1. Institute of Information Theory and Automation, Prague, Czech Republic

    Jiřina Vejnarová

  2. Insight Centre for Data Analytics, School of Computer Science and IT University College Cork, Cork, Ireland

    Nic Wilson

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Mailly, JG. (2021). Constrained Incomplete Argumentation Frameworks. In: Vejnarová, J., Wilson, N. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2021. Lecture Notes in Computer Science(), vol 12897. Springer, Cham. https://doi.org/10.1007/978-3-030-86772-0_8

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  • DOI: https://doi.org/10.1007/978-3-030-86772-0_8

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