On predicate constraints with efficiently solvable task of fitting to training set

The work is dedicated to classification of predicate constraints that arise in supervised learning. Suppose that supplementary constraints are given in the form of predicate pair. Then the characteristic property of supervised learning is that it require efficient algorithm to find a function preserving this pair and behaving on the training set maximally similar to the known dependence. We deal with classification of constraints that allow such algorithm. One of approaches to this problem is to classify constraints with respect to type of predicates on a range set. This approach has connections with relational and functional clones of multi-valued logic. In the boolean case complete classification was obtained. In general case, practically important class of order predicates was introduced and it was shown that this class is efficiently solvable.