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Non-Monotonic Inference Properties for Assumption-Based Argumentation

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Theory and Applications of Formal Argumentation (TAFA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9524))

Abstract

Cumulative Transitivity and Cautious Monotonicity are widely considered as important properties of non-monotonic inference and equally as regards to information change. We propose three novel formulations of each of these properties for Assumption-Based Argumentation (ABA)—an established structured argumentation formalism, and investigate these properties under a variety of ABA semantics.

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Notes

  1. 1.

    The modification of the rules in \(\mathcal {F}'\) is required to preserve flatness. We also slightly abuse the notation by using \(\overline{}\) for both contrary mappings: the implicit presumption is that the original contrary mapping \(\overline{}\) is extended with the assignment \(\overline{\psi } = y\), where y is new to \(\mathcal {L}\).

  2. 2.

    Again, for brevity reasons, the same symbol \(\overline{}\) is used for both contrary mappings: in \(\mathcal {F}'\), the original contrary mapping \(\overline{}\) is implicitly restricted to a diminished set of assumptions.

  3. 3.

    Deduction(s) \(\varPhi \vdash ^{R} \varphi \) with \(\psi \in \varPhi \) are replaced with the deduction(s) \(\varPhi \setminus \{ \psi \} \vdash ^{R' \cup \{ \psi \leftarrow \top \}} \varphi \) such that \(R' \subseteq R\) is the set of rules from R that do not contain \(\psi \) in their bodies.

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Author information

Authors and Affiliations

  1. Imperial College London, London, UK

    Kristijonas Čyras & Francesca Toni

Authors
  1. Kristijonas Čyras
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  2. Francesca Toni
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Corresponding author

Correspondence to Kristijonas Čyras .

Editor information

Editors and Affiliations

  1. King's College London, London, United Kingdom

    Elizabeth Black

  2. Strand Building;Strand Campus, King's College London, London, United Kingdom

    Sanjay Modgil

  3. Department of Computing Science, University of Aberdeen, Aberdeen, United Kingdom

    Nir Oren

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Čyras, K., Toni, F. (2015). Non-Monotonic Inference Properties for Assumption-Based Argumentation. In: Black, E., Modgil, S., Oren, N. (eds) Theory and Applications of Formal Argumentation. TAFA 2015. Lecture Notes in Computer Science(), vol 9524. Springer, Cham. https://doi.org/10.1007/978-3-319-28460-6_6

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  • DOI: https://doi.org/10.1007/978-3-319-28460-6_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28459-0

  • Online ISBN: 978-3-319-28460-6

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