Formal theories and linguistic descriptions

In this contribution, we discuss properties which a formal logical theory (we call it the theory of evaluating expressions) should have to serve us as a tool for modeling of the meaning of a certain class of natural language expressions called evaluating (linguistic) expressions. We further construct a formal theory for modeling of the meaning of sets of fuzzy IF–THEN rules (called linguistic descriptions) and finally present a basic schema of fuzzy logic deduction. The basis for our study is first-order fuzzy logic with evaluated syntax.