The complexity of facets resolved
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
The complexity of logic-based abduction
Journal of the ACM (JACM)
ACM Computing Surveys (CSUR)
A logic-based theory of deductive arguments
Artificial Intelligence
A Reasoning Model Based on the Production of Acceptable Arguments
Annals of Mathematics and Artificial Intelligence
Defeasible logic programming: an argumentative approach
Theory and Practice of Logic Programming
Argumentation in artificial intelligence
Artificial Intelligence
Elements of Argumentation
Argumentation in Artificial Intelligence
Argumentation in Artificial Intelligence
The complexity of propositional implication
Information Processing Letters
The Complexity of Circumscriptive Inference in Post's Lattice
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Dialectic proof procedures for assumption-based, admissible argumentation
Artificial Intelligence
The Complexity of the Warranted Formula Problem in Propositional Argumentation
Journal of Logic and Computation
The Complexity of Reasoning for Fragments of Autoepistemic Logic
ACM Transactions on Computational Logic (TOCL)
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Many proposals for logic-based formalizations of argumentation consider an argument as a pair (φ, α), where the support φ is understood as a minimal consistent subset of a given knowledge base which has to entail the claim α. In most scenarios, arguments are given in the full language of classical propositional logic which makes reasoning in such frameworks a computationally costly task. For instance, the problem of deciding whether there exists a support for a given claim has been shown to be Σ2P-complete. In order to better understand the sources of complexity (and to identify tractable fragments), we focus on arguments given over formulae in which the allowed connectives are taken from certain sets of Boolean functions. We provide a complexity classification for four different decision problems (existence of a support, checking the validity of an argument, relevance and dispensability) with respect to all possible sets of Boolean functions.