Communications of the ACM
Applications of circumscription to formalizing common-sense knowledge
Artificial Intelligence
A theory of diagnosis from first principles
Artificial Intelligence
Eliminating the fixed predicates from a circumscription
Artificial Intelligence
Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
Exact learning Boolean functions via the monotone theory
Information and Computation
Oracles and queries that are sufficient for exact learning
Journal of Computer and System Sciences
Artificial Intelligence
Data mining, hypergraph transversals, and machine learning (extended abstract)
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Machine Learning
Machine Learning
Computing Circumscriptive Databases by Integer Programming: Revisited
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
A Demand-Driven Algorithm for Generating Minimal Models
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
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In this paper, we consider a method of computing minimal models in propositional logic. We firstly show that positively minimal disjuncts in DNF (Disjunctive Normal Form) of the original axiom corresponds with minimal models. A disjunct D is positively minimal if there is no disjunct which contains less positive literal than D. We show that using superset query and membership query which were used in some learning algorithms in computational learning theory, we can compute all the minimal models. We then give a restriction and an extension of the method. The restriction is to consider a class of positive (sometimes called monotone) formula where minimization corresponds with diagnosis and other important problems in computer science. Then, we can replace superset query with sampling to give an approximation method. The algorithm itself has been already proposed by [Valiant84], but we show that the algorithm can be used to approximate a set of minimal models as well. On the other hand, the extension is to consider circumscription with varied propositions. We show that we can compute equivalent formula of circumscription using a similar technique to the above.