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Logical Argumentation Principles, Sequents, and Nondeterministic Matrices

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Logic, Rationality, and Interaction (LORI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10455))

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Abstract

The concept of “argumentative consequence” is introduced, involving only the attack relations in Dung-style abstract argumentation frames. Collections of attack principles of different strength, referring to the logical structure of claims of arguments, lead to new characterizations of classical and nonclassical consequence relations. In this manner systematic relations between structural constraints on abstract argumentation frames, sequent rules, and nondeterministic matrix semantics for corresponding calculi emerge.

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Notes

  1. 1.

    Of course, the idea to label arguments in an argumentation frame with formulas is not new (see, e.g., [6, 12, 13]). We use the labels to highlight the logical form of concrete claims, while abstracting away from their particular support or any specific form of attack.

  2. 2.

    The same formula may occur as claim of different arguments. Thus we (implictly) refer to occurrences of formulas, rather than to formulas themselves when talking about attacks in a given SAF.

  3. 3.

    Note that, if we identify arguments with counter-models and if S contains all relevant counter-models, then argumentative consequence coincides with ordinary logical consequence: every counter-model of the conclusion must invalidate some premise.

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Acknowledgments

We like to thank Stefan Woltran and the referees for interesting suggestions regarding related work.

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Authors and Affiliations

  1. Institut für Computersprachen, Vienna University of Technology, Favortitenstr. 9-11, 1040, Vienna, Austria

    Esther Anna Corsi & Christian G. Fermüller

Authors
  1. Esther Anna Corsi
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  2. Christian G. Fermüller
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Corresponding author

Correspondence to Christian G. Fermüller .

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Editors and Affiliations

  1. Institute for Logic, Language and Computation, University of Amsterdam , Amsterdam, Noord-Holland, The Netherlands

    Alexandru Baltag

  2. Department of Philosophy, The University of Auckland, Auckland, Auckland, New Zealand

    Jeremy Seligman

  3. Graduate School of Letters, Hokkaido University , Sapporo, Japan

    Tomoyuki Yamada

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Corsi, E.A., Fermüller, C.G. (2017). Logical Argumentation Principles, Sequents, and Nondeterministic Matrices. In: Baltag, A., Seligman, J., Yamada, T. (eds) Logic, Rationality, and Interaction. LORI 2017. Lecture Notes in Computer Science(), vol 10455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55665-8_29

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  • DOI: https://doi.org/10.1007/978-3-662-55665-8_29

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  • Print ISBN: 978-3-662-55664-1

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