In the decision making systems logical equations are obtained that have no solution in the frame of the classic propositional logic (r-logic). Solution of these problems is proposed by introducing an extended imaginary logic (i-logic) and constructing a complex logic (s-logic). An additional axiom is stated between the real and imaginary logics connecting their states. The three logics - r, i, and s, satisfy the requirements of the Boolean algebra and e lattice.