Modal Logic is an extension of more formal logic. It is an attempt to use modal elements to form logic structures that are not absolute. For example terms such as probability, possibilities, necessity are elements of modal logic.
Modal Logic Examples
Peaceful discourse is a probable element of middle east peace.
Peaceful discourse is a necessity for middle east peace.
Middle east peace is a possibility with peaceful discourse.
Above I purposefully used a very complex example with many variables. Modal logic can be comprised of very complex logic structures. The above examples might be comprised of thousands of mathematical equations. Modal logic has a semantic vocabulary and axiomatic system which forms its logic and arguments.