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A pattern is a set of binary or ternary relations. A description of the pattern is a formula of many sorted predicate calculus with metric spaces defined on indices of predicate constants which is satisfied by the given pattern. The pattern recognition problem is to find whether the formula is satisfied by the given relation. The pattern description problem is to form from the given pattern the corresponding formula. To solve this problem usual training methods1 are applied together with techniques used for program synthesis2. The limitations imposed by these techniques imply limitations to our approach.

On pattern recognition and description using many sorted predicate calculi