Semantical considerations on nonmonotonic logic
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Artificial Intelligence
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A graph-theoretic approach to default logic
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Default theories that always have extensions
Artificial Intelligence
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Mixed integer programming methods for computing nonmonotonic deductive databases
Journal of the ACM (JACM)
Soundness and completeness of a logic programming approach to default logic
AAAI'94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 2)
Structure-driven algorithms for truth maintenance
Artificial Intelligence
Default reasoning using classical logic
Artificial Intelligence
Stable models and non-determinism in logic programs with negation
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Nonmonotonic Logic: Context-Dependent Reasoning
Nonmonotonic Logic: Context-Dependent Reasoning
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IEEE Transactions on Knowledge and Data Engineering
Reasoning with Stratified Default Theories
LPNMR '95 Proceedings of the Third International Conference on Logic Programming and Nonmonotonic Reasoning
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
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Artificial Intelligence
An incremental algorithm for generating all minimal models
Artificial Intelligence
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IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
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Finding the stable models of a knowledge base is a significant computational problem in artificial intelligence. This task is at the computational heart of truth maintenance systems, autoepistemic logic, and default logic. Unfortunately, it is NP-hard. In this paper we present a hierarchy of classes of knowledge bases, Ω1, Ω2,..., with the following properties: first, Ω1 is the class of all stratified knowledge bases; second, if a knowledge base Π is in Ωk, then Π has at most k stable models, and all of them may be found in time O(lnk), where l is the length of the knowledge base and n the number of atoms in Π, third, for an arbitrary knowledge base Π, we can find the minimum k such that Π belongs to Ωk in time polynomial in the size of Π, and, last, where κ is the class of all knowledge bases, it is the case that ∪i=1∞ Ωi= κ, that is, every knowledge base belongs to some class in the hierarchy.