Measure Refutations and Metrics on Statements of Experts (Logical Formulas) in the Models for Some Theory

* This work was financially supported by the Russian Foundation for Basic Research, project no. 04-01-00858a.

The paper discusses a logical expert statements represented as the formulas with probabilities of the first order language consistent with some theory T. Theoretical-models methods for setting metrics on such statements are offered. Properties of metrics are investigated. The research allows solve problems of the best reconciliation of expert statements, constructions of decision functions in pattern recognition, creations the bases of knowledge and development of expert systems.