Complex Multivalue Logic with Two Sequentially Connected Logic Structure

The present work proposes and investigates a method for building a complex multi-valued logic, including two sequentially connected propositional logics: real L
r
with two states T and F, and imaginary L
i
with states i and ¬i. The four states are not equivalent to each other. At the same time, the multi-valued logic is not built hierarchically. Imaginary logic is completely superior in truth to real logic. This is achieved by additional constraints between states F and i. Research results have been obtained for the proposed multivalued logic model. It is shown that the three logics - L
r
, L
i
and L
s
correspond to the axioms of the Boolean algebra and the distributive lattice. Some possibilities for the use of these multivalued logics in research and applied fields are pointed out.