In this paper our aim is to provide a short survey of main historical developments of systems of fuzzy logic in narrow sense, today under the umbrella of the discipline called Mathematical Fuzzy Logic, arising from the birth of Zadeh{\textquoteright}s fuzzy sets in 1965. Particular attention is devoted to show how the tools of mathematical logic have allowed to define logical systems which form the core of Mathematical Fuzzy Logic and allow for a formalization of some topics included in Zadeh{\textquoteright}s agenda spanning from fuzzy sets to approximate reasoning and probability theory of fuzzy events.

}, author = {Tommaso Flaminio and Francesc Esteva and Llu{\'\i}s Godo} }