On Modalities for Vague Notions

We examine modal logical systems, with generalized operators, for the precise treatment of vague notions such as ‘often’, ‘a meaningful subset of a whole’, ‘most’, ‘generally’ etc. The intuition of ‘most’ as “all but for a ‘negligible’ set of exceptions” is made precise by means of filters. We examine a modal logic, with a new modality for a local version of ‘most’ and present a sound and complete axiom system. We also discuss some variants of this modal logic.