Sets of Boolean Connectives That Make Argumentation Easier

  • Nadia Creignou
  • Johannes Schmidt
  • Michael Thomas
  • Stefan Woltran
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6341)

Abstract

Many proposals for logic-based formalizations of argumentation consider an argument as a pair (Φ,α), where the support Φ is understood as a minimal consistent subset of a given knowledge base which has to entail the claim α. In most scenarios, arguments are given in the full language of classical propositional logic which makes reasoning in such frameworks a computationally costly task. For instance, the problem of deciding whether there exists a support for a given claim has been shown to be \(\Sigma^\mathrm{p}_2\)-complete. In order to better understand the sources of complexity (and to identify tractable fragments), we focus on arguments given over formulae in which the allowed connectives are taken from certain sets of Boolean functions. We provide a complexity classification for four different decision problems (existence of a support, checking the validity of an argument, relevance and dispensability) with respect to all possible sets of Boolean functions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Nadia Creignou
    • 1
  • Johannes Schmidt
    • 1
  • Michael Thomas
    • 2
  • Stefan Woltran
    • 3
  1. 1.LIF, UMR CNRS 6166Aix-Marseille UniversitéMarseille Cedex 9France
  2. 2.Institut für Theoretische InformatikGottfried Wilhelm Leibniz UniversitätHannoverGermany
  3. 3.Institut für Informationssysteme E184/2Technische Universität WienWienAustria

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