**Section 1**

**Theory** 

**1** 

*Italy* 

Gaetano Licata

*Università degli Studi di Palermo* 

**Fuzzy Logic, Knowledge and Natural Language** 

This is an introductive study on what Fuzzy Logic is, on the difference between Fuzzy Logic and the other many-valued calculi and on the possible relationship between Fuzzy Logic and the complex sciences. Fuzzy Logic is nowadays a very popular logic methodology. Different kinds of applications in cybernetics, in software programming and its growing use in medicine seems to make Fuzzy Logic, according to someone, the "new" logic of science and technology. In his enthusiastic panegyric of Fuzzy Logic, Kosko (1993) argues that after thirty years from the birth of this calculus, it is time to declare the new era of Fuzzy Logic and to forget the old era of classical logic. I think that this point of view is too much simplistic. However, it is true that Fuzzy Logic and many valued-logics are connected with a new ontology. Quantum physics and biology of complexity push the research in the direction of a new and more complex concept of logical formalization. The ontological vagueness must be connected to the logical vagueness, the undetermined development of some natural phenomena must be treated with many-valued logic. The importance and usefulness of many-valued logic in science will be showed by two examples: i) the unforeseeability in biology (theory of Prigogine), ii) the birth of quantum mechanics and the employment of probabilistic logic in the interpretation of the wave-function. Kosko affirms that Fuzzy Logic is the solution to the fact that science proposes a linear image of a nonlinear world and quotes the Heisenberg's indeterminacy principle. Moreover Kosko proposes a fuzzy alternative to the probabilistic interpretation of the equation of Schrödinger. I think that Fuzzy Logic is an important device to face the new ontology of complexity, but this does not entail that Fuzzy Logic is the solution to all the scientific problems. It is useful to understand why Fuzzy Logic created this illusion and which can be

One of the most important argument employed by Kosko to underline the superiority of Fuzzy Logic (against classical and probabilistic logic) is its similarity with natural language (henceforth NL) and natural thinking. The relaxations of the pretences of logical truth, in classical sense, seem to give Fuzzy Logic the character of natural thinking, with its imprecision and its approximation, and also with its richness. In my work I will argue that Fuzzy Logic is a very useful device to treat natural phenomena and quantities in a logical way, and that Fuzzy Logic is a very versatile many-valued logic because the number of truth values can vary from few to infinite, at will of the user. Nevertheless, I will argue also that Fuzzy Logic is not the key of the formalization of NL, and that the phenomena of vagueness and the relaxations of classical logical truth, which Fuzzy Logic can treat, are only one

**1. Introduction** 

its real place in scientific methodology.
