New model metrics between relations of n-valued logic and uncertainty of automatic clustering of statements

Abstract

Statements that can be recorded by logical multivalued relations are studied. Using model theory, we introduce relations such that various logical values are taken into account most completely in the distances between relations of Lukasevich n-valued logic, introduce an uncertainty measure for statements, and formulate and prove theorems about the properties of these values. Using the introduced distances and uncertainty measures, we adapt known clustering algorithms for the clustering of sets of statements and use examples to examine results for various values of n. We study collective distances, which are the most effective in the sense of clustering indices and can be used to generate new distances for more powerful sets of statements.