Algorithms and Complexity Results for Persuasive Argumentation

  • Authors:

  • Eun Jung Kim;Sebastian Ordyniak;Stefan Szeider

  • Affiliations:

  • Department of Computer Science, Royal Holloway, University of London, UK;Institute of Information Systems, Vienna University of Technology, Austria;Institute of Information Systems, Vienna University of Technology, Austria

  • Venue:
  • Proceedings of the 2010 conference on Computational Models of Argument: Proceedings of COMMA 2010
  • Year:
  • 2010

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Abstract

Value-based argumentation frameworks, as introduced by Bench-Capon, allow the abstract representation of persuasive argumentation. This formalism takes into account the relative strength of arguments with respect to some ordering which represents an audience. Deciding subjective or objective acceptance (i.e., acceptance with respect to at least one or with respect to all orderings) are intractable computational problems. In this paper we study the computational complexity of testing the subjective or objective acceptance for problem instances that obey certain restrictions. We consider structural restrictions in terms of the underlying graph structure of the value-based argumentation framework and in terms of properties of the equivalence relation formed by arguments with the same relative strength. We identify new tractable fragments where subjective and objective acceptance can be tested in polynomial time. Furthermore we show the intractability of some fragments that are located at the boundary to tractability. Our results disprove two conjectures of Dunne (Artificial Intelligence 171, 2007).