Outcome of contradictions in the models of historical phenomena

Mathematic models of real, particularly historical phenomena, are as a rule extremely complicated, and systems of limitation corresponding to them are contradictory that entails the necessity of correcting procedures. A brief review of approaches to correction of such systems developed by the authors and basing on the theory of discrete generalized solution of inconsistent limitation systems and collective methods of teaching to image detecting is offered in the article. The research is implemented under the interdisciplinary program of the Urals Department of RAS 'Historical dynamics of Russia: factors, models, forecast'.