The complexity of optimization problems
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
SIAM Journal on Computing
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
Hard problems for simple default logics
Artificial Intelligence - Special issue on knowledge representation
NP trees and Carnap's modal logic
Journal of the ACM (JACM)
The complexity of default reasoning under the stationary fixed point semantics
Information and Computation
Is intractability of nonmonotonic reasoning a real drawback?
Artificial Intelligence
Monotonic reductions, representative equivalence, and compilation of intractable problems
Journal of the ACM (JACM)
Reasoning with Incomplete Information
Reasoning with Incomplete Information
Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
A survey on knowledge compilation
AI Communications
Complexity results for restricted credulous default reasoning
AI Communications
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Model checking for nonmonotonic logics: algorithms and complexity
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
Complexity Results for 2CNF Default Theories
Fundamenta Informaticae
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In this paper we analyze the problem of checking whether a default theory has a single extension. This problem is important for at least three reasons. First, if a theory has a single extension, nonmonotonic inference can be reduced to entailment in propositional logic (which is computationally easier) using the set of consequences of the generating defaults. Second, a theory with many extensions is typically weak i.e., it has few consequences; this indicates that the theory is of little use, and that new information has to be added to it, either as new formulae, or as preferences over defaults. Third, some applications require as few extensions as possible (e.g. diagnosis). We study the complexity of checking whether a default theory has a single extension. We consider the combination of several restrictions of default logics: seminormal, normal, disjunction-free, unary, ordered. Complexity varies from the first to the third level of the polynomial hierarchy. The problem of checking whether a theory has a given number of extensions is also discussed.