Fuzzy-Set Based Logics — an History-Oriented Presentation of their Main Developments [chapter]

Didier Dubois, Francesc Esteva, Lluís Godo, Henri Prade
2007 Handbook of the History of Logic  
The representation of human-originated information and the formalization of commonsense reasoning has motivated different schools of research in Artificial or Computational Intelligence in the second half of the 20th century. This new trend has also put formal logic, originally developed in connection with the foundations of mathematics, in a completely new perspective, as a tool for processing information on computers. Logic has traditionally put emphasis on symbolic processing at the
more » ... al level and binary truth-values at the semantical level. The idea of fuzzy sets introduced in the early sixties [Zadeh, 1965] and the development of fuzzy logic later on [Zadeh, 1975a] has brought forward a new formal framework for capturing graded imprecision in information representation and reasoning devices. Indeed, fuzzy sets membership grades can be interpreted in various ways which play a role in human reasoning, such as levels of intensity, similarity degrees, levels of uncertainty, and degrees of preference. Of course, the development of fuzzy sets and fuzzy logic takes its roots in concerns already encountered in non-classical logics in the first half of the century, when the need for intermediary truth-values and modalities emerged. We start by briefly surveying some of the main issues raised by this research line before describing the historical development of fuzzy sets, fuzzy logic and related issues. Jan Lukasiewicz (1878Lukasiewicz ( -1956 and his followers have developed three-valued logics, and other many-valued systems, since 1920 [ Lukasiewicz, 1920] . This research was motivated by philosophical concerns as well as some technical problems in logic but not so much by issues in knowledge representation, leaving the interpretation of intermediate truth-values unclear. This issue can be related to a misunderstanding regarding the law of excluded middle and the law of non-contradiction, and the connections between many-valued logics and modal logics. The principle of bivalence, Every proposition is either true or false,
doi:10.1016/s1874-5857(07)80009-4 fatcat:s4i5zfomgzbxnfbuif5ffsesea