History
Some particular t-norm fuzzy logics have been introduced and investigated long before the family was recognized (even before the notions of fuzzy logic or t-norm emerged):
- Łukasiewicz logic (the logic of the Łukasiewicz t-norm) was originally defined by Jan Łukasiewicz (1920) as a three-valued logic; it was later generalized to n-valued (for all finite n) as well as infinitely-many-valued variants, both propositional and first-order.
- Gödel–Dummett logic (the logic of the minimum t-norm) was implicit in Gödel's 1932 proof of infinite-valuedness of intuitionistic logic. Later (1959) it was explicitly studied by Dummett who proved a completeness theorem for the logic.
A systematic study of particular t-norm fuzzy logics and their classes began with Hájek's (1998) monograph Metamathematics of Fuzzy Logic, which presented the notion of the logic of a continuous t-norm, the logics of the three basic continuous t-norms (Łukasiewicz, Gödel, and product), and the 'basic' fuzzy logic BL of all continuous t-norms (all of them both propositional and first-order). The book also started the investigation of fuzzy logics as non-classical logics with Hilbert-style calculi, algebraic semantics, and metamathematical properties known from other logics (completeness theorems, deduction theorems, complexity, etc.).
Since then, a plethora of t-norm fuzzy logics have been introduced and their metamathematical properties have been investigated. Some of the most important t-norm fuzzy logics were introduced in 2001, by Esteva and Godo (MTL, IMTL, SMTL, NM, WNM), Esteva, Godo, and Montagna (propositional ŁΠ), and Cintula (first-order ŁΠ).
Read more about this topic: T-norm Fuzzy Logics
Famous quotes containing the word history:
“The thing that struck me forcefully was the feeling of great age about the place. Standing on that old parade ground, which is now a cricket field, I could feel the dead generations crowding me. Here was the oldest settlement of freedmen in the Western world, no doubt. Men who had thrown off the bands of slavery by their own courage and ingenuity. The courage and daring of the Maroons strike like a purple beam across the history of Jamaica.”
—Zora Neale Hurston (1891–1960)
“The history of our era is the nauseating and repulsive history of the crucifixion of the procreative body for the glorification of the spirit.”
—D.H. (David Herbert)
“Both place and time were changed, and I dwelt nearer to those parts of the universe and to those eras in history which had most attracted me.”
—Henry David Thoreau (1817–1862)