Applications for boolean logic operations in zero-one integer linear programming (ILP) It is nice to know that every boolean formula can be expressed by zero-one
integer programming by this answered question. But are there any applications?

To be more precise: Are there papers which use the existense of zero-one
integer programming for boolean operations?
Yes, there are many applications.  To find some, go to that question and look through the linked and related questions on the sidebar; that will already show you several applications.  Next, do a search for the search term "ILP" on this site, and browse through the search results.  You will find many examples of problems that can be solved with zero-one ILP using these techniques.