Читать книгу Introduction to Fuzzy Logic - James K. Peckol - Страница 61

Plato was among the first to attempt to quantify an alternative possible state of existence. He proposed the existence of a third region, beyond TRUE and FALSE, in which “opposites tumbled about.” Many modern philosophers such as Bertrand Russell, Kurt Gödel, G.W. Leibniz, and Hermann Lotze have supported Plato's early ideas.

The first formal steps away from classical logic were taken by the Polish mathematician Lukasiewicz (also the inventor of Reverse Polish Notation, RPN). He proposed a three‐valued logic in which the third value, called possible, was to be assigned a numeric value somewhere between TRUE and FALSE. Lukasiewicz also developed an entire set of notations and an axiomatic system for his logic. His intention was to derive modern mathematics.

In later works, he also explored four‐ and five‐valued logics before declaring that there was nothing to prevent the development of infinite‐valued logics. Donald Knuth proposed a similar three‐valued logic and suggested using the values of −1, 0, 1. The idea never received much support.