The KleeneRosser Paradox, The Liar's Paradox & A Fuzzy Logic Programming Paradox Imply SAT is (NOT) NPcomplete
Abstract
After examining the {\bf P} versus {\bf NP} problem against the KleeneRosser paradox of the $\lambda$calculus [94], it was found that it represents a counterexample to NPcompleteness. 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 2valued instance of a fuzzy logic programming paradox discovered in the system of [90]. Three proofs that show that {\bf SAT} is (NOT) NPcomplete are presented. The counterexample classes to NPcompleteness are also counterexamples to Fagin's theorem [36] and the ImmermannVardi theorem [89,110], the fundamental results of descriptive complexity. All these results show that {\bf ZF$\not$C} is inconsistent.
 Publication:

arXiv eprints
 Pub Date:
 June 2008
 arXiv:
 arXiv:0806.2947
 Bibcode:
 2008arXiv0806.2947E
 Keywords:

 Computer Science  Logic in Computer Science
 EPrint:
 Submitted to the ACM Transactions on Computation Theory