  We consider an example of four valued semantics partially inspired by quantum
computations and negation-like operations occurred therein. In particular we
consider a representation of so called square root of negation within this four
valued semantics as an operation which acts like a cycling negation. We define
two variants of logical matrices performing different orders over the set of
truth values. Purely formal logical result of our study consists in
axiomatizing the logics of defined matrices as the systems of binary
consequence relation and proving correctness and completeness theorems for
these deductive systems.
