Semantical considerations on nonmonotonic logic
Artificial Intelligence
A logical framework for default reasoning
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Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
An assumption-based framework for non-monotonic reasoning
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Dialectic semantics for argumentation frameworks
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Coherence in finite argument systems
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Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part II
Argumentation-Based Proof Procedures for Credulous and Sceptical Non-monotonic Reasoning
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Assumption-Based Argumentation for Epistemic and Practical Reasoning
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SDKB'10 Proceedings of the 4th international conference on Semantics in data and knowledge bases
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Modelling argument accrual with possibilistic uncertainty in a logic programming setting
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ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Probabilistic qualification of attack in abstract argumentation
International Journal of Approximate Reasoning
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We present a family of dialectic proof procedures for the admissibility semantics of assumption-based argumentation. These proof procedures are defined for any conventional logic formulated as a collection of inference rules and show how any such logic can be extended to a dialectic argumentation system. The proof procedures find a set of assumptions, to defend a given belief, by starting from an initial set of assumptions that supports an argument for the belief and adding defending assumptions incrementally to counter-attack all attacks. The proof procedures share the same notion of winning strategy for a dispute and differ only in the search strategy they use for finding it. The novelty of our approach lies mainly in its use of backward reasoning to construct arguments and potential arguments, and the fact that the proponent and opponent can attack one another before an argument is completed. The definition of winning strategy can be implemented directly as a non-deterministic program, whose search strategy implements the search for defences.