Hard problems for simple default logics
Artificial Intelligence - Special issue on knowledge representation
On the decidability and complexity of autoepistemic reasoning
Fundamenta Informaticae - Special issue on modal logics in knowledge representation
Closure properties of constraints
Journal of the ACM (JACM)
Theories of computability
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Yet some more complexity results for default logic
Artificial Intelligence
Default Logic as a Query Language
IEEE Transactions on Knowledge and Data Engineering
Equivalence and Isomorphism for Boolean Constraint Satisfaction
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Complexity Results for 2CNF Default Theories
Fundamenta Informaticae
Propositional abduction is almost always hard
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Information Processing Letters
What makes propositional abduction tractable
Artificial Intelligence
Boolean Constraint Satisfaction Problems: When Does Post's Lattice Help?
Complexity of Constraints
The Complexity of Reasoning for Fragments of Default Logic
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Trichotomy Results on the Complexity of Reasoning with Disjunctive Logic Programs
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Trichotomy and dichotomy results on the complexity of reasoning with disjunctive logic programs
Theory and Practice of Logic Programming
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Reiter's default logic formalizes nonmonotonic reasoning using default assumptions. The semantics of a given instance of default logic is based on a fixpoint equation defining an extension. Three different reasoning problems arise in the context of default logic, namely the existence of an extension, the presence of a given formula in an extension, and the occurrence of a formula in all extensions. Since the end of 1980s, several complexity results have been published concerning these default reasoning problems for different syntactic classes of formulas.We derive in this paper a complete classification of default logic reasoning problems by means of universal algebra tools using Post's clone lattice. In particular we prove a trichotomy theorem for the existence of an extension, classifying this problem to be either polynomial, NP-complete, or Σ2P-complete, depending on the set of underlying Boolean connectives. We also prove similar trichotomy theorems for the two other algorithmic problems in connection with default logic reasoning.