Many-valued logic

In 1932 Gödel defined[4] a family of many-valued logics, with finitely many truth values , for example has the truth values and has . Implication and negation were defined by Jan Łukasiewicz through the following functions:

At first Łukasiewicz used these definition in 1920 for his three-valued logic , with truth values . [5]

By adopting truth values defined in the same way as for Gödel logics , it is possible to create a finitely-valued family of logics , the abovementioned and the logic , in which the truth values are given by the rational numbers in the interval .

Source: en.wikipedia.org