Partial First-order Logic with Approximative Functors Based on Properties

In the present paper a logically exact way is presented in order to define approximative functors on object level in the partial first–order logic relying on approximation spaces. By the help of defined approximative functors one can determine what kind of approximations has to be taken into consideration in the evaluating process of a formula. The representations of concepts (properties) of our available knowledge can be used to approximate not only any concept (property) but any relation. In the last section lower and upper characteristic matrixes are introduced. These can be very useful in different applications.