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We present various new concepts and results related to abstract dialectical frameworks (ADFs), a powerful generalization of Dung's argumentation frameworks (AFs). In particular, we show how the existing definitions of stable and preferred semantics which are restricted to the subcase of so-called bi-polar ADFs can be improved and generalized to arbitrary(More)
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argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of(More)
We provide a solution to the ramification problem that integrates findings of different axiomatic approaches to ramification from the last ten to fifteen years. For the first time, we present a solution that: (1) is independent of a particular time structure, (2) is formulated in classical first-order logic, (3) treats cycles – a notoriously difficult(More)
We provide a systematic in-depth study of the semantics of abstract dialectical frameworks (ADFs), a recent generalisation of Dung's abstract argumentation frameworks. This is done by associating with an ADF its characteristic one-step consequence operator and defining various semantics for ADFs as different fixpoints of this operator. We first show that(More)
dialectical frameworks (ADFs) have recently been proposed as a versatile generalization of Dung's abstract argumentation frameworks (AFs). In this paper, we present a comprehensive analysis of the computational complexity of ADFs. Our results show that while ADFs are one level up in the polynomial hierarchy compared to AFs, there is a useful subclass of(More)
Fuzzy reasoning is a very productive research field that during the last years has provided a number of theoretical approaches and practical implementation prototypes. Nevertheless, the classical implementations , like Fril, are not adapted to the latest formal approaches, like multi-adjoint logic semantics. Some promising implementations, like Fuzzy(More)