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Abstract Argumentation via Monadic Second Order Logic

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNAI,volume 7520)

Abstract

We propose the formalism of Monadic Second Order Logic (MSO) as a unifying framework for representing and reasoning with various semantics of abstract argumentation. We express a wide range of semantics within the proposed framework, including the standard semantics due to Dung, semi-stable, stage, cf2, and resolution-based semantics. We provide building blocks which make it easy and straight-forward to express further semantics and reasoning tasks. Our results show that MSO can serve as a lingua franca for abstract argumentation that directly yields to complexity results. In particular, we obtain that for argumentation frameworks with certain structural properties the main computational problems with respect to MSO-expressible semantics can all be solved in linear time. Furthermore, we provide a novel characterization of resolution-based grounded semantics.

Keywords

  • Unify Framework
  • Order Logic
  • Argumentation Framework
  • Complete Extension
  • Attack Relation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Dvořák’s and Woltran’s work has been funded by the Vienna Science and Technology Fund (WWTF) through project ICT08-028 and Szeider’s work has been funded by the European Research Council (ERC), grant reference 239962 (COMPLEX REASON).

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Dvořák, W., Szeider, S., Woltran, S. (2012). Abstract Argumentation via Monadic Second Order Logic. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds) Scalable Uncertainty Management. SUM 2012. Lecture Notes in Computer Science(), vol 7520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33362-0_7

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  • DOI: https://doi.org/10.1007/978-3-642-33362-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33361-3

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