Applications of circumscription to formalizing common-sense knowledge
Artificial Intelligence
Artificial Intelligence
Unification as a complexity measure for logic programming
Journal of Logic Programming
Some computational aspects of circumscription
Journal of the ACM (JACM)
A rational reconstruction of nonmonotonic truth maintenance systems (research note)
Artificial Intelligence
The complexity of model checking for circumscriptive formulae
Information Processing Letters
Characterizing diagnoses and systems
Artificial Intelligence
Propositional circumscription and extended closed-world reasoning are &Pgr;p2-complete
Theoretical Computer Science
Mixed integer programming methods for computing nonmonotonic deductive databases
Journal of the ACM (JACM)
Reasoning with minimal models: efficient algorithms and applications
Artificial Intelligence
Extending and implementing the stable model semantics
Artificial Intelligence
Positive Unit Hyperresolution Tableaux and Their Application to Minimal Model Generation
Journal of Automated Reasoning
On Indefinite Databases and the Closed World Assumption
Proceedings of the 6th Conference on Automated Deduction
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Enhancing disjunctive logic programming systems by SAT checkers
Artificial Intelligence
A hierarchy of tractable subsets for computing stable models
Journal of Artificial Intelligence Research
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
The Quadrupel --A Model for Automating Intermediary Selection in Supply Chain Management
Proceedings of the 2011 conference on Information Modelling and Knowledge Bases XXII
On the tractability of minimal model computation for some CNF theories
Artificial Intelligence
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The task of generating minimal models of a knowledge base is at the computational heart of diagnosis systems like truth maintenance systems, and of nonmonotonic systems like autoepistemic logic, default logic, and disjunctive logic programs. Unfortunately, it is NP-hard. In this paper we present a hierarchy of classes of knowledge bases, @J"1,@J"2,...@?, with the following properties: first, @J"1 is the class of all Horn knowledge bases; second, if a knowledge base T is in @J"k, then T has at most k minimal models, and all of them may be found in time O(lk^2), where l is the length of the knowledge base; third, for an arbitrary knowledge base T, we can find the minimum k such that T belongs to @J"k in time polynomial in the size of T; and, last, where K is the class of all knowledge bases, it is the case that @?"i"="1^~@J"i=K, that is, every knowledge base belongs to some class in the hierarchy. The algorithm is incremental, that is, it is capable of generating one model at a time.