A comprehensive theory of trichotomous evaluative linguistic expressions

In this paper, a logical theory of the, so-called, trichotomous evaluative linguistic expressions (TEv-expressions) is presented. These are frequent expressions of natural language, such as “small, very small, roughly medium, extremely big”, etc. The theory is developed using the formal system of higher-order fuzzy logic, namely the fuzzy type theory (generalization of classical type theory). First, we discuss informally what are properties of the meaning of TEv-expressions. Then we construct step by step axioms of a formal logical theory TEv of TEv-expressions and prove various properties of TEv. All the proofs are syntactical and so, our theory is very general. We also outline construction of a canonical model of TEv. The main elegancy of our theory consists in the fact that semantics of all kinds of evaluative expressions is modeled in a unified way. We also prove theorems demonstrating that essential properties of the vagueness phenomenon can be captured within our theory.