Formal concept analysis is an important tool for knowledge representation and mining， and formal context is one of the basic concepts in formal concept analysis. A new attribute reduction — inner product reduction was proposed to solve the problem of whether the object set in the formal context has the same attribute in a given attribute set， and also to solve the problem of how to eliminate irrelevant attributes in the calculation. Firstly， the concept of inner product was given in formal context. Then， the reduction theory and method in relation system were used to define the inner product reduction， and the inner product reduction algorithm based on discernibility matrix was proposed to obtain all the reduction results in the formal context， and the reduction core was obtained through the intersection operation based on the results. In addition， when attributes increased， an incremental inner product reduction algorithm was designed. Finally， the application of inner product reduction was explored in infectious disease network. In the simulated case， 6 attributes were reduced to 2 attributes. Simulation outcomes demonstrate that the inner product reduction method is feasible， interpretable， and successful in achieving the knowledge reduction goal.