The Logic of Probability: A Trip through Uncertainty

In real life we have to deal with uncertainty, imprecision
and vagueness. Many ideas were introduced and studied in
detail to manage with these problems. Now we briefly ex pose the main formal concepts which describe non-ideal
situations, i.e. Probability, Statistics and Fuzzy Logic.
Probability has recent origins with respect to other branch es of mathematics which have deep roots in the past, like
geometry or algebra.
We may say all this started with Antoine Gombaud,
Chevalier de Méré (1607–1684), who asked Blaise Pascal
(1623–1662) about gambling with dice. The correspond ence between Pierre de Fermat and Blaise Pascal, which
began in 1654, initially on these questions, led to the intro duction of basic concepts, i.e. probability and expectation.
Only in 1657, Christian Huygens in "De Ratiociniis in ludo
aleae" proposed a first systematic study of the new branch
of mathematics. However, the need of an axiomatic con struction of the theory of probability arose to analyze more
general and complex situations than gambling. A strong
formalization was supplied by the monograph "Founda tions of the theory of probability" (1933) by Andrey
Nikolaevich Kolmogorov.
Statistics represent the most popular application of proba bility theory, providing research tools in several areas, in cluding physical and natural sciences, technology, psy chology, economics and medicine. Statistics are the bridge
that connects experimental data to the mathematical theory
behind itself.
Fuzzy logic, sometime confused with probability, wants to
express and formalize all the sentences which are not true
or false at all; the philosophical idea is that "everything is a
matter of degree" (Zadeh).