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Journal of Logic and Computation Advance Access published online on June 26, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp032
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Towards a Common Framework for Dialectical Proof Procedures in Abstract Argumentation

Phan Minh Thang, Phan Minh Dung and Nguyen Duy Hung

Department of Computer Science, Asian Institute of Technology, GPO Box 4, Klong Luang, Pathumthani 12120, Thailand.
E-mail: thangfm{at}ait.ac.th; dung{at}cs.ait.ac.th; nguyenduy.hung{at}ait.ac.th


  Abstract

We present a common framework for dialectical proof procedures for computing credulous, grounded, ideal and sceptical preferred semantics of abstract argumentation. The framework is based on the notions of dispute derivation and base derivation. Dispute derivation is a dialectical notion first introduced for computing credulous semantics in assumption-based argumentation, and adapted here for computing credulous semantics and grounded semantics. Base derivation is introduced for two purposes: (i) to characterize all preferred extensions containing a given argument, and (ii) to represent backtracking in the search for a dispute derivation. We prove the soundness of the proof procedures for any argumentation frameworks and their completeness for general classes of finitary or finite-branching argumentation frameworks containing the class of finite argumentation frameworks as a subclass.We also discuss related results.

Keywords: Abstract argumentation; dialectical; proof procedure; dispute resolution


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