  Smarandache (2003) introduced a new set-valued fuzzy logic called
(nonstandard) neutrosophic logic by using Robinson's nonstandard analysis.
However, its definition involved many errors including the illegal use of
nonstandard analysis. In this paper, we provide a rigorous definition of
neutrosophic logic. All the errors in the original definition are addressed. We
then point out some paradoxes of neutrosophic logic. Finally we formulate
neutrosophic logic with no use of nonstandard analysis.
