Modules exhibit logical cohesion when elements are grouped together because they are related in some way logically. Even though the functionality of logically cohesive modules might be of the same general category, they may be different in other ways. For this reason, this type of cohesion is considered low. While better than coincidental cohesion, these types of modules are not very cohesive.
An example of logical cohesion would be a module that contains a set of functions that handles I/O for the application. While they are related logically, the nature of the various functions would be quite different. They would be more cohesive if each type of I/O was handled by a separate module.