Describes formal accounts of modal logic in which the evaluation of a modal operator admits degrees and are able to make finer distinctions than, e.g., necessity and possibility operators alone. Natural examples of graded modality appear in the context of deontic logic, in which it is reasonable to believe that obligations admit degrees, that is, some obligations are stronger or weaker than others. A more formal example is the notion of numerical possibility, in which operators ${♢}_n$ are introduced corresponding to the truth condition:

• • ${♢}_n\phi$ is true at $w$ if there are $n$ many accessible worlds at which $\phi$ is true

or the related operator ${♢}_f$ with the truth condition:

• • ${♢}_f\phi$ is true at $w$ if there are finitely many accessible worlds at which $\phi$ is true.