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Johannes Wallner

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AAAI Conference 2018 Conference Paper

Weighted Abstract Dialectical Frameworks

Gerhard Brewka
Hannes Strass
Johannes Wallner
Stefan Woltran

Abstract Dialectical Frameworks (ADFs) generalize Dung’s argumentation frameworks allowing various relationships among arguments to be expressed in a systematic way. We further generalize ADFs so as to accommodate arbitrary acceptance degrees for the arguments. This makes ADFs applicable in domains where both the initial status of arguments and their relationship are only insufﬁciently speciﬁed by Boolean functions. We deﬁne all standard ADF semantics for the weighted case, including grounded, preferred and stable semantics. We illustrate our approach using acceptance degrees from the unit interval and show how other valuation structures can be integrated. In each case it is sufﬁcient to specify how the generalized acceptance conditions are represented by formulas, and to specify the information ordering underlying the characteristic ADF operator. We also present complexity results for problems related to weighted ADFs.

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AAAI Conference 2016 Conference Paper

Complexity Results and Algorithms for Extension Enforcement in Abstract Argumentation

Johannes Wallner
Andreas Niskanen
Matti Järvisalo

Understanding the dynamics of argumentation frameworks (AFs) is important in the study of argumentation in AI. In this work, we focus on the so-called extension enforcement problem in abstract argumentation. We provide a nearly complete computational complexity map of ﬁxed-argument extension enforcement under various major AF semantics, with results ranging from polynomial-time algorithms to completeness for the second-level of the polynomial hierarchy. Complementing the complexity results, we propose algorithms for NP-hard extension enforcement based on constrained optimization. Going beyond NP, we propose novel counterexample-guided abstraction reﬁnement procedures for the second-level complete problems and present empirical results on a prototype system constituting the ﬁrst approach to extension enforcement in its generality.

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