Modal logic is a type of formal logic primarily developed in the 1960s that extends classical
propositional and
predicate logic to include operators expressing
modality. Modals—words that express modalities—qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is
usually happy, in which case the term "usually" is functioning as a modal. The traditional
alethic modalities, or modalities of truth, include
possibility ("Possibly, p", "It is possible that p"), necessity ("Necessarily, p", "It is necessary that p"), and impossibility ("Impossibly, p", "It is impossible that p"). Other modalities that have been formalized in modal logic include
temporal modalities, or modalities of time (notably, "It was the case that p", "It has always been that p", "It will be that p", "It will always be that p"),
deontic modalities (notably, "It is obligatory that p", and "It is permissible that p"),
epistemic modalities, or modalities of knowledge ("It is known that p") and
doxastic modalities, or modalities of belief ("It is believed that p").