Correct algorithms in the algebraic closure of a family of recognition algorithms with a special kind of information teaching

The completeness problem is solved for a set of recognition algorithms of a special kind. These algorithms use as teaching information a collection of “conditional” inequalities between classes. It is shown that the algebraic closure of these recognition algorithms contains an algorithm correctly solving every permissible problem; the order of this closure is calculated and the correct algorithm in the closure is found in explicit form.