On the syntactico-semantical completeness of first-order fuzzy logic. II. Main results

The extension of fuzzy theories is studied and the important deduction theorem is proved which is a generalisation of the corresponding classical one. Algebraic properties of the set of formulae are studied. This section serves as a preparation for the proofs of the most important theorems in this paper which are the completeness theorems being generalisation of the famous Godel's ones in classical logic. At last, some theorems on completion of fuzzy theories are proved