Modal logic

Modal logic is a kind of logic used to represent statements about necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causation. For instance, in epistemic modal logic, the formula ◻ P {\displaystyle \Box P} can be used to represent the statement that P {\displaystyle P} is known. In deontic modal logic, that same formula can represent that P {\displaystyle P} is a moral obligation. Modal logic considers the inferences that modal statements give rise to. For instance, most epistemic modal logics treat the formula ◻ P → P {\displaystyle \Box P\rightarrow P} as a tautology, representing the principle that only true statements can count as knowledge. However, this formula is not a tautology in deontic modal logic, since what ought to be true can be false.