Judgment Aggregation in Abstract Dialectical Frameworks
Abstract dialectical frameworks (ADFs) are a knowledge representation formalism introduced as a generalisation of Dung’s abstract argumentation frameworks (AFs) by Gerhard Brewka and co-authors. We look at a judgment aggregation problem in ADFs, namely the problem of aggregating a profile of complete interpretations. We generalise the family of interval aggregation methods, studied in the AF case in our previous work, to the ADF case. Along the way we define the notions of down-admissible and up-complete interpretations, that were already previously defined for the AF case by Caminada and Pigozzi. These aggregation methods may open the way to define interesting new semantics for ADFs, such as a generalisation to the ADF case of the ideal semantics for AFs.
KeywordsAbstract dialectical frameworks argumentation frameworks judgment aggregation interval methods
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