Applications of circumscription to formalizing common-sense knowledge
Artificial Intelligence
Results on translating defaults to circumscription
Artificial Intelligence
Logic programs with classical negation
Logic programming
Relating disjunctive logic programs to default theories
Proceedings of the second international workshop on Logic programming and non-monotonic reasoning
Handbook of logic in artificial intelligence and logic programming (vol. 1)
Handbook of logic in artificial intelligence and logic programming (vol. 1)
Proceedings of the eleventh international conference on Logic programming
A shorter model theory
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
Nonmonotonic Logic: Context-Dependent Reasoning
Nonmonotonic Logic: Context-Dependent Reasoning
(De)Composition of Situation Calculus Theories
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Reasoning with incomplete information: investigations of non-monotonic reasoning
Reasoning with incomplete information: investigations of non-monotonic reasoning
Model-based diagnosis using structured system descriptions
Journal of Artificial Intelligence Research
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
Theorem proving with structured theories
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Logic-based subsumption architecture
Artificial Intelligence - Special issue on logical formalizations and commonsense reasoning
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Craig's interpolation theorem [3] is an important theorem known for propositional logic and first-order logic. It says that if a logical formula 脽 logically follows from a formula 驴, then there is a formula 驴, including only symbols that appear in both 驴, 脽, such that 脽 logically follows from 驴 and 驴 logically follows from 驴. Such theorems are important and useful for understanding those logics in which they hold as well as for speeding up reasoning with theories in those logics. In this paper we present interpolation theorems in this spirit for three nonmonotonic systems: circumscription, default logic and logic programs with the stable models semantics (a.k.a. answer set semantics). These results give us better understanding of those logics, especially in contrast to their nonmonotonic characteristics. They suggest that some monotonicity principle holds despite the failure of classic monotonicity for these logics. Also, they sometimes allow us to use methods for the decomposition of reasoning for these systems, possibly increasing their applicability and tractability. Finally, they allow us to build structured representations that use those logics.