A Double Negation Operator in Logic $N^*$

An axiomatization of double Routley negation operator as a necessity operator in logic $N^*$ is obtained. Logic $N^{\sharp}$ describing the behavior of double Routley negation operator is introduced, its Kripke semantics is defined, completeness wrt to this semantics is proved as well as its finite approximation property and decidability. Constructive properties of logics $N^*$ and $N^{\sharp}$ are compared.