Modal logic is a branch of logic that deals with the concepts of possibility and necessity. It is concerned with the relationship between what is possible and what is necessary, and how these concepts can be expressed in language.

In modal logic, a possible world is a world that is consistent with the laws of logic. It is a world in which the laws of logic hold true, and in which the facts of the world are different from the facts of the actual world.

In modal logic, necessity is something that is true in all possible worlds, while possibility is something that is true in at least one possible world. For example, the statement "It is necessary that 2 + 2 = 4" is true because 2 + 2 = 4 is true in all possible worlds. The statement "It is possible that the sky is green" is true because there is at least one possible world in which the sky is green.

Modal logic can be used to analyze the meaning of natural language sentences by identifying the possible worlds in which the sentence is true. For example, the sentence "It is possible that the sky is green" is true if and only if there is at least one possible world in which the sky is green. The sentence "It is necessary that 2 + 2 = 4" is true if and only if there are no possible worlds in which 2 + 2 does not equal 4.

A modal adverb is an adverb that expresses a modal concept, such as possibility, necessity, probability, or certainty. The word "possibly" is an example of a modal adverb because it expresses the modal concept of possibility.

Modal logic and deontic logic are two branches of logic that overlap in some areas. Modal logic is concerned with the concepts of possibility and necessity, while deontic logic is concerned with the concepts of obligation, permission, and prohibition. The two branches of logic overlap in the area of moral necessity, which is the idea that some actions are morally necessary or morally permissible.

A deontic modal is a modal that expresses a deontic concept, such as obligation, permission, or prohibition. The word "obligatory" is an example of a deontic modal because it expresses the deontic concept of obligation.

Modal logic and epistemic logic are two branches of logic that overlap in some areas. Modal logic is concerned with the concepts of possibility and necessity, while epistemic logic is concerned with the concepts of knowledge, belief, and doubt. The two branches of logic overlap in the area of epistemic possibility, which is the idea that something is possible given what is known or believed.

An epistemic modal is a modal that expresses an epistemic concept, such as knowledge, belief, or doubt. The word "knowingly" is an example of an epistemic modal because it expresses the epistemic concept of knowledge.

Modal logic and temporal logic are two branches of logic that overlap in some areas. Modal logic is concerned with the concepts of possibility and necessity, while temporal logic is concerned with the concepts of time and tense. The two branches of logic overlap in the area of temporal possibility, which is the idea that something is possible at some point in time.

A temporal modal is a modal that expresses a temporal concept, such as time or tense. The word "eventually" is an example of a temporal modal because it expresses the temporal concept of time.

Modal logic and dynamic logic are two branches of logic that overlap in some areas. Modal logic is concerned with the concepts of possibility and necessity, while dynamic logic is concerned with the concepts of action and change. The two branches of logic overlap in the area of dynamic possibility, which is the idea that something is possible as a result of some action or change.

A dynamic modal is a modal that expresses a dynamic concept, such as action or change. The word "causally" is an example of a dynamic modal because it expresses the dynamic concept of causation.

Modal logic and belief logic are two branches of logic that overlap in some areas. Modal logic is concerned with the concepts of possibility and necessity, while belief logic is concerned with the concepts of belief and disbelief. The two branches of logic overlap in the area of doxastic possibility, which is the idea that something is possible according to someone's beliefs.

A belief modal is a modal that expresses a belief concept, such as belief or disbelief. The word "believably" is an example of a belief modal because it expresses the belief concept of belief.