Modal logic is a branch of formal logic that deals with the concepts of necessity, possibility, and contingency. In modal logic, these concepts are expressed using modal operators, such as "◊" (diamond) and "□" (box), which are applied to statements or propositions.

The diamond operator "◊" is typically used to express possibility, indicating that a statement is true in at least one possible world. For example, the statement "It is possible that it will rain tomorrow" can be expressed in modal logic as "◊(It will rain tomorrow)". The box operator "□", on the other hand, is used to express necessity, indicating that a statement is true in all possible worlds. For example, the statement "It is necessary that 2+2=4" can be expressed in modal logic as "□(2+2=4)".

Modal logic allows for the formal analysis of many philosophical concepts, such as knowledge, belief, obligation, and time. For example, epistemic modal logic deals with the logical properties of knowledge and belief, while deontic modal logic deals with the logical properties of obligation and permission. Temporal modal logic deals with the logical properties of time and change.

Modal logic also has applications in computer science, artificial intelligence, and game theory. It is used in formal verification of computer systems and software, as well as in reasoning about strategies and actions in multi-agent systems.