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The complexity of default reasoning under the stationary fixed point semantics
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Artificial Intelligence
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Theoretical Computer Science
Stable models and non-determinism in logic programs with negation
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Artificial Intelligence
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Proceedings of the 2008 conference on Computational Models of Argument: Proceedings of COMMA 2008
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Dialectic proof procedures for assumption-based, admissible argumentation
Artificial Intelligence
The computational complexity of ideal semantics
Artificial Intelligence
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FoIKS'08 Proceedings of the 5th international conference on Foundations of information and knowledge systems
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Artificial Intelligence
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Bondarenko et al. have recently proposed an abstract framework for default reasoning. Besides capturing most existing formalisms and proving that their standard semantics all coincide, the framework extends these formalisms by generalising the semantics of admissible and preferred arguments, originally proposed for logic programming only.In this paper we analyse the computational complexity of credulous and sceptical reasoning under the semantics of admissible and preferred arguments for (the propositional variant of) the instances of the abstract framework capturing theorist, circumscription, logic programming, default logic, and autoepistemic logic. Although the new semantics have been tacitly assumed to mitigate the computational hardness of default reasoning under the standard semantics of stable extensions, we show that in many cases reasoning under the admissibility and preferability semantics is computationally harder than under the standard semantics. In particular, in the case of autoepistemic logic, sceptical reasoning under preferred arguments is located at the fourth level of the polynomial hierarchy, whereas the same form of reasoning under stable extensions is located at the second level.