The reachability, observability, and detectability w.r.t. arbitrary inputs of Boolean control networks (BCNs) are investigated via the semi-tensor product of matrices. The reachability w.r.t. arbitrary inputs of BCNs is studied . The definitions of the reachability and set reachability w.r.t. arbitrary inputs are proposed, and the reachability matrix and set reachability matrix w.r.t. arbitrary inputs are constructed to check the reachability and set reachability of BCNs. As applications of the set reachability w.r.t. arbitrary inputs, the observability and detectability with arbitrary inputs of BCNs are then studied. Necessary and sufficient conditions for the observability and detectability w.r.t. arbitrary inputs of BCNs are obtained. Finally, numerical examples are given to illustrate the obtained theoretical results.