1 research outputs found
The Kleene-Rosser Paradox, The Liar's Paradox & A Fuzzy Logic Programming Paradox Imply SAT is (NOT) NP-complete
After examining the {\bf P} versus {\bf NP} problem against the Kleene-Rosser
paradox of the -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 ZFC} is inconsistent.Comment: Submitted to the ACM Transactions on Computation Theor