Interpolative realization of Boolean algebra frame for consistent treatment of gradation and/or fuzziness

The new approach to treating gradation in logic, theory of sets, relations etc., is based on interpolative realization of finite Boolean algebra (IBA). IBA has a crucially different approach to gradation compared to fuzzy approaches. Technically, as any element of finite Boolean algebra can be represent in a canonical disjunctive form it can also be represented in the form of a corresponding generalized Boolean polynomial. A generalized Boolean polynomial can process values from a real unit interval [0, 1]. So, all laws of Boolean algebra are preserved in the case of gradation