Philosophical logic
Philiosophers use arguments to talk about the concepts and ideas they have. In order to connect these arguments and ideas, and to be able to convince people, they need logic. This kind of logic is known as philosophical logic. The logic can be what is called classical logic, but it can also be more complex, such as modal logic. What is commonly used is propositional logic, which extends the classical logic and introduces quantifiiers.
There is also a philiosophy of logic, which is slightly different.
The term philosphical logic is often used to contrast it with mathematical logic, which is used in the natural sciences.