Distances and Uncertainty (Unauthentic) Measures on Propositions of $n$-Valued Logic

We consider formulas of $n$-valued logic. Such formulas could be used as records of experts' judgments We use methods of mathematical logic and model theory for $n$-valued logic to define metrics on formulas (propositions) and uncertainty measures. We study properties of such metrics and measures. The novelties of this paper are the definition of metrics on the classes of equivalent formulas and the definition of uncertainty (unauthentic) measures together with finding their good properties. We also note their importance for cluster analysis, creating of deciding functions and pattern recognition.