Fuzzy Natural Logic: Towards Mathematical Logic of Human Reasoning

Abstract

AbstractOne 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. Of course, this cannot be realized without cooperation with linguists. On the other hand, it seems reasonable not to try to solve all the problems raised by the linguistic research but rather to develop a simplified model that would capture the main features of the semantics of natural language and thus made it possible to realize sophisticated technical applications. In the paper, we will show that basic formalism of FNL has already been established and has potential for further development. We also outline how model of the meaning of basic constituents of natural language (nouns, adjectives, adverbs, verbs) can be developed and the human-like reasoning can proceed.KeywordsNatural LanguageNoun PhraseLinguistic ExpressionGradable AdjectiveLinguistic DescriptionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.