On the Metrics on Multi-Valuable Logical Expression and Application of the Metrics in Databases

The article discusses models and formulas of multivalued logics having various applications in model theory and knowledge bases, and, in particular, for recording ambiguous statements of experts (logical knowledge base). Using methods mathematical logic and model theory for multi-valued logics, theorems on rich collections of formulas (types) are obtained without assuming the stability of the (complete, metric) model, but with the condition on the class of its extensions with the same (continuous)theory, orthogonal cases are considered. We consider formulas of manyvalued logic. Further are « distances » on formulas (statements) and degrees (measures) nontriviality (uncertainty) of the formula, as a measure of the formula’s infidelity on the class models under consideration (possible worlds). The properties of the introduced distances and measures of nontriviality (uncertainty) of formulas on classes of multivalued models. Methods autora proposed assignment on classes of nonequivalent formulas of metrics, degrees of nontriviality (uncertainty) and set useful properties for them, which are used in algorithms clustering, the construction of deciding functions, pattern recognition and the question of standards in artificial intelligence. From this description of all possible metrics is given for a fixed class of finite-valued models of a fixed many-valued logic and / or its weakening (by reducing the list of axioms).