A package for testing the Boolean algebra relationships is proposed. The language of implementation is Planner. The same language is used as input one. The output digital data are presented in form of lists, and the Boolean relations issued in LaTeX notation. The consideration is based on four-valued Boolean algebra. It connects to an attempt to resolve Russell's paradox taking into consideration such properties of logical assertion as properties to be 'non-truth' and 'non-false' or 'truth' and 'false' simultaneously, besides usual properties to be 'truth' or 'false'. In thus obtained logic the number of possibilities to connect couples of such variables is close to 4.5 billions instead of 16 in usual two-valued logic. Some matrix representations of these connections and algebraic relationships are introduced. Formerly the relationships, which took place in single-valued and double-valued logics, were affirmed. Then the formulas of expanded four-valued logic were considered and set of new tautologies were confirmed. This logic allows to extend some relationships by introducing the alternative functions of logic, which do not obey the Prege axioms, but are relative to corresponding functions of expanded logic. In particular the reflexive law of implication and equivalence is invalid in such an extended logic. New form of the law of excluded middle appears in this logic. Such a form gives a possible explanation of Russell's paradox. Many tautologies, which take place in expanded logic, transform to extended ones.
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