Semantical considerations on nonmonotonic logic
Artificial Intelligence
On the relation between default and autoepistemic logic
Artificial Intelligence
Translating default logic into standard autoepistemic logic
Journal of the ACM (JACM)
Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning
Logic-based artificial intelligence
Fixpoint semantics for logic programming a survey
Theoretical Computer Science
On the intertranslatability of non-monotonic logics
Annals of Mathematics and Artificial Intelligence
Uniform semantic treatment of default and autoepistemic logics
Artificial Intelligence
Ultimate approximation and its application in nonmonotonic knowledge representation systems
Information and Computation
On the evaluation of argumentation formalisms
Artificial Intelligence
The Carneades model of argument and burden of proof
Artificial Intelligence
Reasoning about preferences in argumentation frameworks
Artificial Intelligence
A system for defeasible argumentation, with defeasible priorities
Artificial intelligence today
Carneades and Abstract Dialectical Frameworks: A Reconstruction
Proceedings of the 2010 conference on Computational Models of Argument: Proceedings of COMMA 2010
An Algorithm for Stage Semantics
Proceedings of the 2010 conference on Computational Models of Argument: Proceedings of COMMA 2010
Argumentation and answer set programming
Logic programming, knowledge representation, and nonmonotonic reasoning
On the issue of reinstatement in argumentation
JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
Relating the semantics of abstract dialectical frameworks and standard AFs
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Relating Carneades with abstract argumentation
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Fundamenta Informaticae - Logic, Language, Information and Computation
Abstract dialectical frameworks revisited
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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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 several existing semantical notions are faithfully captured by our definition, then proceed to define new ADF semantics and show that they are proper generalisations of existing argumentation semantics from the literature. Most remarkably, this operator-based approach allows us to compare ADFs to related nonmonotonic formalisms like Dung argumentation frameworks and propositional logic programs. We use polynomial, faithful and modular translations to relate the formalisms, and our results show that both abstract argumentation frameworks and abstract dialectical frameworks are at most as expressive as propositional normal logic programs.