The last decade has seen an enormous development in infinite-valued
systems and in particular in such systems which have become known as
mathematical fuzzy logics.
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The paper discusses the mathematical background for the interest in
such systems of mathematical fuzzy logics, as well as the most
important ones of them. It concentrates on the propositional cases,
and mentions the first-order systems more superficially. The main
ideas, however, become clear already in this restricted setting.