Relating the Semantics of Abstract Dialectical Frameworks and Standard AFs

Brewka, Gerhard; Dunne, Paul E.; Woltran, Stefan

doi:10.5591/978-1-57735-516-8/IJCAI11-137

Relating the Semantics of Abstract Dialectical Frameworks and Standard AFs

Gerhard Brewka, Paul E. Dunne, Stefan Woltran

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Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence. Pages 780-784.

https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-137

Abstract

One criticism often advanced against abstract argumentation frameworks (AFs), is that these consider only one form of interaction between atomic arguments: specifically that an argument attacks another. Attempts to broaden the class of relationships include bipolar frameworks, where arguments support others, and abstract dialectical frameworks (ADFs). The latter, allow acceptance'' of an argument, x, to be predicated on a given propositional function, C_x, dependent on the corresponding acceptance of its parents, i.e. those y for which occurs. Although offering a richly expressive formalism subsuming both standard and bipolar AFs, an issue that arises with ADFs is whether this expressiveness is achieved in a manner that would be infeasible within standard AFs. Can the semantics used in ADFs be mapped to some AF semantics? How many arguments are needed in an AF to simulate'' an ADF? We show that (in a formally defined sense) any ADF can be simulated by an AF of similar size and that this translation can be realised by a polynomial time algorithm.

Gerhard Brewka, Paul E. Dunne, and Stefan Woltran. 2011. Relating the Semantics of Abstract Dialectical Frameworks and Standard AFs. In Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI-11. IJCAI, 780–784. https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-137

@inproceedings{ijcai2011p137,
  title     = {Relating the Semantics of Abstract Dialectical Frameworks and Standard AFs},
  author    = {Brewka, Gerhard and Dunne, Paul E. and Woltran, Stefan},
  booktitle = {Proceedings of the Twenty-Second International Joint Conference on
               Artificial Intelligence, {IJCAI-11}},
  publisher = {AAAI Press/International Joint Conferences on Artificial Intelligence},
  editor    = {Toby Walsh},
  pages     = {780--784},
  year      = {2011},
  month     = {7},
  doi       = {10.5591/978-1-57735-516-8/IJCAI11-137},
  url       = {https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-137},
}

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TI  - Relating the Semantics of Abstract Dialectical Frameworks and Standard AFs
AU  - Brewka, Gerhard
AU  - Dunne, Paul E.
AU  - Woltran, Stefan
T2  - Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI-11
PB  - AAAI Press/International Joint Conferences on Artificial Intelligence
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DO  - 10.5591/978-1-57735-516-8/IJCAI11-137
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