Abstract: In this world there are basically two different processes: One is quantity-based process such as moving body, heat transfer etc., which are described by differential (difference) equations. The other one is logic-based process such as plying chess, decision-making etc. Many efficient tools have been developed to handle the former, but so far there are still limited tools to deal with the later. Using semi-tensor product of matrix and the matrix expression of logical functions, the logical equations can be converted into algebraic equations, and the dynamics of a logical (control) system can be converted into a discrete-time linear (bilinear control) system. Under this framework, the topological structure of a logical dynamic system can be revealed. Moreover, when the logical control systems, such as Boolean control networks, are considered, some basis control problems, including controllability, observability, realization disturbance decoupling, stability and stabilization ect. can be investigated and properly solved. The method can also be used to infinitely repeated games to find Nash (sub-Nash) solutions.