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Abstract: Circumscription and the closed world assumption with its variants are well-known 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... (Update)
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...pg preferred. Hardness : Given a 3 sat instance S and a literal l, it is P hard to decide whether l is true in a minimal model of S [3]. We construct a LPOD t(S) such that l is true in a fi; pg preferred answer set of t(S) i l is true in a minimal model of S. t(S) f :A 1...
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BibTeX entry: (Update)
Eiter, T., and G. Gottlob. 1993. Propositional Circumscription and Extended Closed World Reasoning are \Pi p 2 -complete. Theoretical Computer Science 114:231--245. http://citeseer.ist.psu.edu/eiter93propositional.html More
@article{ eiter93propositional,
author = "Thomas Eiter and Georg Gottlob",
title = "Propositional circumscription and extended closed-world reasoning are {$\Pi^P_2$}-complete",
journal = "Theoretical Computer Science",
volume = "114",
number = "2",
pages = "231--245",
year = "1993",
url = "citeseer.ist.psu.edu/eiter93propositional.html" }
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40 and Sparse Turing-Complete Sets for NP (context) - Kadin - 1989
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29 Some Computational Aspects of Circumscription (context) - Kolaitis, Papadimitriou - 1990
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