We say that an n-argument predicate P ~ .O n is finite, if P is a finite set. Note that the set of individuals .O is infinite! Finite predicates are useful in data bases and in finite mathematics. The logic DBL proposed here operates on finite predicates only. Y~re construct an imbedding for DBJb in a special modal logic MPZ. We prove that if a finite predicate is expressible in the classical logic, it is also expressible in DBL. Quantifiers are not necessary in DB]5. Some simple algebraic properties of DBZ arc indicated. Some mathematical problems concerning, in particular, finite groups, finite geometries [1] etc., may be formulated with the help of finite predicates, i.e. predicates, wlfich are finite sets. The classical predicate logic CPL seems to be superfluous for treating such problems, since there may arise infinite predicates by the problem solving.
The data base design and exploitation [2] form a real reservation for finite predicates. The CPJ5 is superfluous here too. As an example, the 1-argument predicate "to be a 3Ietro employee" is finite and can be kept in data base. But the classical negation of this predicate is a practically infinite predicate, its cardinal number is about four billion. It cannot be kept in data base. It is natural to design a logic where all the predicates will be finite. The logic DBL, proposed below, may be useful for a preliminary analysis.