A QBF-based Formalization of Abstract Argumentation Semantics

Ofer Arieli, Martin W.A. Caminada

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)
9 Downloads (Pure)


We introduce a unified logical theory, based on signed theories and Quantified Boolean Formulas (QBFs) that can serve as the basis for representing and computing various argumentation-based decision problems. It is shown that within our framework we are able to model, in a simple and modular way, a wide range of semantics for abstract argumentation theory. This includes complete, grounded, preferred, stable, semi-stable, stage, ideal and eager semantics. Further more, our approach is purely logical, making for instance decision problems like skeptical and credulous acceptance of arguments simply a matter of entailment and satisfiability checking. The latter may be verified by off-the-shelf QBF-solvers.
Original languageEnglish
Pages (from-to)229-252
Number of pages24
JournalJournal of Applied Logic
Issue number2
Early online date21 Mar 2013
Publication statusPublished - Jun 2013

Bibliographical note

Supported by the National Research Fund, Luxembourg (LAAMI project) and by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant ref. EP/J012084/1 (SAsSY project).


  • semantics for abstract argumentation
  • frameworks
  • quantified Boolean formulas
  • signed theories


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