Collective Distances for Clustering N-Valued Logic Formulas Representing Knowledge Base of Intellectual System

The paper considers a problem of the analysis of logical expert statements that arises at the interfaces between artificial intelligence, machine learning and mathematical logic. Within the framework of the logic-based modelling in knowledge representation, the propositions stored in the knowledge base of an intellectual system are described using formulas of some logic. The paper investigates the properties of metrics and measures of non-triviality on the formulas of $n$-valued logic; the notion of collective metrics is proposed. The introduced concepts are used for cluster analysis of logical statements; examples of the obtained solutions are described.