A LOGICAL APPROACH TO QUALITATIVE REASONING WITH 'SEVERAL'

We examine logical systems, with generalized quantifiers, for expressing and reasoning about (some versions of) 'several'. The primary motivation is a qualitative approach to assertions and arguments involving vague notions, found in ordinary language and in some branches of science. Intuitions underlying (versions of) 'several' are made precise by means of families of subsets. This gives a conservative extension of classical first-order logic, with which it shares various properties. Its sorted version captures relative notions with appropriate behavior.