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van Gijzel, Bas; Nilsson, Henrik (2014)
Publisher: IOS Press
Languages: English
Types: Article
Argumentation theory combines philosophical concepts and computational models to deliver a practical approach to reasoning that handles uncertain information and possibly conflicting viewpoints. This paper focuses on the structured approach to argumentation that incorporates domain specific knowledge and argumentation schemes. There is a lack of implementations and implementation methods for most structured models. This paper shows how taking a principled approach, using the programming language Haskell, helps addressing this problem. We construct a framework for developing structured argumentation models and translations between models (given intertranslatability of models). We furthermore provide a methodology to quickly test and formally prove desirable properties of such implementations using a theorem prover. We demonstrate our approach on the Carneades argumentation model and Dung's abstract argumentation frameworks, implementing both the models and a translation from Carneades into AFs. We then provide implementations of correspondence properties and an initial formalisation of Dung's AFs into a theorem prover. The final result is a verified pipeline from the structured model Carneades into existing efficient SAT-based implementations of Dung's AFs.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] Gerhard Brewka, Paul E. Dunne, and Stefan Woltran. Relating the semantics of abstract dialectical frameworks and standard AFs. In Proceedings of the 22nd International Joint Conference on Arti cial Intelligence (IJCAI-11), pages 780{785, 2011.
    • [2] Gerhard Brewka and Thomas F. Gordon. Carneades and abstract dialectical frameworks: A reconstruction. In Massimiliano Giacomin and Guillermo R. Simari, editors, Computational Models of Argument. Proceedings of COMMA 2010, pages 3{12, Amsterdam etc, 2010. IOS Press 2010.
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    • [9] Bas van Gijzel and Henrik Nilsson. Haskell gets argumentative. In Proceedings of the Symposium on Trends in Functional Programming (TFP 2012), LNCS 7829, pages 215{ 230, St Andrews, UK, 2013. LNCS.
    • [10] Bas van Gijzel and Henrik Nilsson. Towards a framework for the implementation and veri cation of translations between argumentation models. In Accepted for Post Proceedings of the 25th symposium on Implementation and Application of Functional Languages (IFL 2013), 2014.
    • [11] Bas van Gijzel and Henry Prakken. Relating Carneades with abstract argumentation via the ASPIC+ framework for structured argumentation. Argument & Computation, 3(1):21{47, 2012.
    • [12] Thomas F. Gordon and Douglas Walton. Proof burdens and standards. In Guillermo Simari and Iyad Rahwan, editors, Argumentation in Arti cial Intelligence, pages 239{258. Springer US, 2009.
    • [13] Sanjay Modgil and Henry Prakken. A general account of argumentation with preferences. Arti cial Intelligence, 195:361{397, 2013.
    • [14] Victor Noel and Antonis Kakas. Gorgias-c: Extending argumentation with constraint solving. In Esra Erdem, Fangzhen Lin, and Torsten Schaub, editors, Logic Programming and Nonmonotonic Reasoning, volume 5753 of Lecture Notes in Computer Science, pages 535{541. Springer Berlin Heidelberg, 2009.
    • [15] Henry Prakken. An abstract framework for argumentation with structured arguments. Argument & Computation, 1:93{124, 2010.
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