Mathematical fuzzy logic; Natural logic

One of the often repeated proclaims appearing in the papers on fuzzy sets and fuzzy logic is their ability to model semantics of some linguistic expressions so that the inherent vagueness of the former is also captured. Recall that this direction of research was initiated 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. In this paper we argue that the potential of fuzzy set theory and fuzzy logic is strong enough to enable developing not only a working model of linguistic semantics but even more --- to develop a model of natural human reasoning that proceeds in natural language. We bring forward 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.