The notion of self-typing is extended with the semantic constraints expressed as sentences. Specifying these behavioral properties is far beyond the expressiveness of type systems. The cornerstone of the approach is the view of classes as theories. The inheritance of class constraints is viewed as a theory morphism. The validity of the results across various possible logics for expressing class constraints is based on the object-oriented view of the notion of an institution. This view ties together the inheritance of class constraints and semantically correct object substitutability. The developed formal system is termed behavioral matching and it is proved to be an institution. Implications of this result are also analyzed.