Fuzzy natural logicFuzzy type theory

One of the proclaims often emphasized in paperson fuzzy sets and fuzzy logic is their ability to model semantics of certain linguistic expressions because their inherent vagueness can be captured by fuzzy sets. This direction of research wasinitiated by L. A. Zadeh already in his early papers and since then, most of the applications of fuzzy sets emphasize presence of natural language, at least in hidden form. Still, this ability isnot generally accepted by linguists. In this paper we try to show that capturing linguistic semantics requires more sophisticatedmodels. One possibility has been elaborated in the concept of fuzzy natural logic (FNL) that is a mathematical theory whose roots lay in the concept of natural logic developed by linguists and logicians. We also argue that it is reasonable to develop a simplified model that would capture the main features of the semantics of natural language and thus make it possible to realize sophisticated technical applications. In the paper, we outline how model of the meaning of basic constituents ofnatural language (nouns, adjectives, adverbs, verbs) has been elaborated in FNL.