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- W1565433391 abstract "After examining the {bf P} versus {bf NP} problem against the Kleene-Rosser paradox of the $lambda$-calculus [94], it was found that it represents a counter-example to NP-completeness. We prove that it contradicts the proof of Cook's theorem. A logical formalization of the liar's paradox leads to the same result. This formalization of the liar's paradox into a computable form is a 2-valued instance of a fuzzy logic programming paradox discovered in the system of [90]. Three proofs that show that {bf SAT} is (NOT) NP-complete are presented. The counter-example classes to NP-completeness are also counter-examples to Fagin's theorem [36] and the Immermann-Vardi theorem [89,110], the fundamental results of descriptive complexity. All these results show that {bf ZF$not$C} is inconsistent." @default.
- W1565433391 created "2016-06-24" @default.
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- W1565433391 date "2008-06-18" @default.
- W1565433391 modified "2023-09-27" @default.
- W1565433391 title "A Paradox Implies SAT is (NOT) NP-complete and ZFC is Inconsistent" @default.
- W1565433391 hasPublicationYear "2008" @default.
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