The task of machine reading comprehension (MRC) is to enable machine to read and understand a piece of text, and then answer the corresponding question correctly. This task requires machine to not only be able to perform semantic understanding, but also possess logical reasoning capabilities. Just like human reading, it involves thinking about the text from two interacting perspectives of semantics and logic. However, previous methods based on reading comprehension either consider only the logical structure of the text or only the semantic structure of the text, and cannot simultaneously balance semantic understanding and logical reasoning. This single form of reasoning cannot make the machine fully understand the meaning of the text. Additionally, the issue of sparsity in composition presents a significant challenge for models that rely on graph-based reasoning. To this end, a cross-graph knowledge propagation network (CGKPN) with adaptive connection is presented to address the above issues. The model first performs self-view node embedding on the constructed logical graph and semantic graph to update the representations of the graphs. Specifically, relevance matrix between nodes is introduced to adaptively adjust node connections in response to the challenge posed by sparse graph. Subsequently, CGKPN conducts cross-graph knowledge propagation on nodes that are identical in both graphs, effectively resolving conflicts arising from identical nodes in different views, and enabling the model to better integrate the logical and semantic relationships of the text through efficient interaction. Experiments on the two MRC datasets ReClor and LogiQA indicate the superior performance of our proposed model CGKPN compared to other existing baselines.