Two Fuzzy Logic Programming Paradoxes Imply Continuum Hypothesis="False" & Axiom of Choice="False" Imply ZFC is Inconsistent

Two different paradoxes of the fuzzy logic programming system of [29] are presented. The first paradox is due to two distinct (contradictory) truth values for every ground atom of FLP, one is syntactical, the other is semantical. The second paradox concerns the cardinality of the valid FLP formulas which is found to have contradictory values: both $\aleph_0$ the cardinality of the natural numbers, and $c$, the cardinality of the continuum. The result is that CH="False" and Axiom of Choice="False". Hence, ZFC is inconsistent.Comment: Submitted to ACM Transactions on Computational Logi

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 $\lambda$-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.Comment: Submitted to the ACM Transactions on Computation Theor