On Modalities for Vague Notions

Mario R. F. BenevidesCarla A. D. M. DelgadoRenata P. de FreitasPaulo A. S. VelosoSheila R. M. Veloso

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.

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