The complexity of sparse sets in P
Proc. of the conference on Structure in complexity theory
On generating all maximal independent sets
Information Processing Letters
Tie-breaking semantics and structural totality
PODS '92 Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
A graph-theoretic approach to default logic
Information and Computation
Default theories that always have extensions
Artificial Intelligence
Graph theoretical structures in logic programs and default theories
Theoretical Computer Science
On Finding Extensions of Default Theories
ICDT '92 Proceedings of the 4th International Conference on Database Theory
Graphs and Hypergraphs
Dialectical Proof Theories for the Credulous Preferred Semantics of Argumentation Frameworks
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Comparing a Pair-Wise Compatibility Heuristic and Relaxed Stratification: Some Preliminary Results
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Preferred Extensions of Argumentation Frameworks: Query Answering and Computation
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Finding kernels or solving SAT
Journal of Discrete Algorithms
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Extensions in prerequisite‐free, disjunction‐free default theories have been shown to be in direct correspondence with kernels of directed graphs; hence default theories without odd cycles always have a “standard” kind of an extension. We show that, although all “standard” extensions can be enumerated explicitly, several other problems remain intractable for such theories: Telling whether a non‐standard extension exists, enumerating all extensions, and finding the minimal standard extension. We also present a new graph‐theoretic algorithm, based on vertex feedback sets, for enumerating all extensions of a general prerequisite‐free, disjunction‐free default theory (possibly with odd cycles). The algorithm empirically performs well for quite large theories.