Artificial intelligence systems require logic calculation to give true or false judgment. However, artificial intelligence systems cannot be simply implemented by basic Boolean logic calculation. Deep artificial neural networks implemented by multiple matrix calculation is one of the efficient methods to construct artificial intelligence systems. We have presented semantic computing models in which input data are mapped in to a semantic space and presented as points in semantic spaces. From the point view of our semantic computing model, the multiple matrix calculation like artificial neural networks is a data mapping operation. That is, input data are mapped into a semantic space by the multiple matrix calculation. In our method, the true or false logic judgement is transmitted into calculating Euclidean distances of those points in the semantic spaces. In order to apply the semantic computation model for developing artificial intelligence systems, it is important to understand the mechanism between the logic calculation and semantic space and the deep-learning mechanism. In this paper, we present logic calculation implemented by the multiple matrix calculation which is the basic calculation method to implement the artificial intelligence system. The most important contribution of this paper is that we first present the mechanism for implementing logic calculation with semantic space model and machine learning. In the paper, we use three example cases to illustrate the mechanism. We first present an example case on implementing combination logic calculations based on linear space mapping. After that, we present an example case where the semantic space is constructed based on principal component analysis. The third example case is on sequential logic operations. The concept of semantic space, subspace selection and learning mechanism utilized in the example cases are also illustrated.