On the syntactico-semantical completeness of first-order fuzzy logic. I. Syntax and semantics

This is the first part of the extensive paper which presents the syntax and semantics of first-order fuzzy logic. We introduce the structure of truth values and present some main properties of its. Then the language of first-order fuzzy logic and its syntax and semantics are defined, and proved many theorems demonstrating their good properties. The concept of a fuzzy theory is defined and the main properties of fuzzy theories are presented including the problem of their consistency and completeness