The Syntactical Proof Of Fuzzy Logic

It is well known that fuzzy logic is generalized from the classic logic and multi-valued logic. Now, fuzzy logic has been widely used in each field of real life, especially in the field of artificial intelligence, automatic control and clustering analysis field. These outstanding achievements make it become the most important research methods and means in the research of uncertainty problems. In recent years, syntactical proof of equivalence has become a new research hotspot in fuzzy logic.Two of the most important research directions of fuzzy logic are semantic and syntactic. Both at home and abroad in the study of fuzzy logic is more concerned about the study of semantic. Base on study of semantics of many logics, completeness of truth-functions and many algebraic problems are solved. Fuzzy logic has achieved impressive research findings, but researches on syntactic of many logics are rare. This paper attempts to change all that by the syntactical proof of equivalence between NM and LWsThe main work of this paper is mainly divided into the following three parts:1. This paper introduces the construction form of fuzzy logic system and its proof theory. On this basis, study the relations among several common formal systems.2. Study the PCP and PP property in IMTL formal system. In the end provides a syntactical proof of equivalence between NM and î–½.3. The previous achievements in the proof of completeness of BL system are discussed. And attempt to prove the completeness of the basic logic BL by a syntactical proof.