Two Fuzzy Logic Programming Paradoxes Imply Continuum Hypothesis="False" & Axiom of Choice="False" Imply ZFC is Inconsistent
Abstract
Description
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.
Submitted to ACM Transactions on Computational Logic
Submitted to ACM Transactions on Computational Logic