Computer Science – Logic in Computer Science
Scientific paper
2008-07-16
Computer Science
Logic in Computer Science
Submitted to ACM Transactions on Computational Logic
Scientific paper
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.
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