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

A complex multivalued hierarchical logic is studied, in which three propositional logics are integrated - one real and two imaginary. They have non-congruent binary states, arranged in descending order of degree of true, obeying the axioms of Boolean algebra and lattice. Analytical dependences are obtained, describing the behavior of the separate states of the complex logic depending on the operations on them - disjunction, conjunction, equivalence and implication. The possible directions for research and application of this class of logical structures are outlined.