Philosophical logicMathematical Logic". It is concerned with characterising notions like inference, rational thought, truth, and contents of thoughts, in the most fundamental ways possible, and trying to model them using modern formal logic.
Philosophical logic is not concerned with the psychological processes connected with thought, or with emotions, images and the like. It is concerned only with those entities — thoughts, sentences, or propositions — that are capable of being true and false. To this extent, though, it does intersect with philosophy of mind and philosophy of language. Gottlob Frege is regarded by many as the founder of modern philosophical logic.