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Complex Multivalued Hierarchical Logic with One Real and Two Imaginary Logical Structures

A complex multivalued hierarchical logic is proposed in which three propositional logics are integrated – one real and two imaginary. The first imaginary logic has “truer” states than the real logic, and the second imaginary logic has even more “truer” states than the first. This leads to hierarchy in the resulting complex multivalued logical structure.It is proved that in the obtained complex logic all axioms of the Boolean algebra and the distribution lattice are fulfilled, without leading to contradictions.The possibilities for applications of the proposed complex logic are stated.