Fuzzy logic, logic programming, and linear logic: towards a new understanding of common sense

Fuzzy logic was originally proposed as a tool for describing human reasoning. Currently, the main area of applications of fuzzy logic is in fuzzy control, where the choice of logic is usually motivated not by logical considerations (i.e. not by what best describes how people actually think), but by purely pragmatic, engineering considerations: what logic would lead to the best control. In this paper, we return to the original meaning of fuzzy logic: a tool for describing human reasoning. We analyze why the existing formalisms are not always adequate, and describe possible modifications of fuzzy logic. Our analysis shows that there are deep similarities between the descriptions of common-sense reasoning in three different fields: fuzzy logic, logic programming and linear logic. Thus, the future formalism for describing human reasoning will probably be a synthesis of these three.