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Propositional Circumscription and Extended Closed World Reasoning are $\Pi^P_2$complete
 Theoretical Computer Science
, 1993
"... Circumscription and the closed world assumption with its variants are wellknown nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction prob ..."
Abstract

Cited by 99 (21 self)
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Circumscription and the closed world assumption with its variants are wellknown nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction problem for arbitrary propositional theories under the extended closed world assumption or under circumscription is $\Pi^P_2$complete, i.e., complete for a class of the second level of the polynomial hierarchy. We answer this question by proving these problems $\Pi^P_2$complete, and we show how this result applies to other variants of closed world reasoning.
The complexity of closed world reasoning and circumscription
 In Proc. 8th AAAI
, 1990
"... Closed world reasoning is a common nonmonotonic technique that allows for dealing with negative information in knowledge and data bases. We present a detailed analysis of the computational complexity of the different forms of closed world reasoning for various fragments of propositional logic. Th ..."
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Cited by 33 (6 self)
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Closed world reasoning is a common nonmonotonic technique that allows for dealing with negative information in knowledge and data bases. We present a detailed analysis of the computational complexity of the different forms of closed world reasoning for various fragments of propositional logic. The analysis allows us to draw a complete picture of the tractability/intractability frontier for such a form of nonmonotonic reasoning. We also discuss how to use our results in order to characterize the computational complexity of other problems related to nonmonotonic inheritance, diagnosis, and default reasoning. 1