Sequent Calculi for ‘Generally’

Logics of ‘generally’ (LG's) were introduced for handling assertions with some versions of vague notions (e.g. ‘generally’, ‘most’, ‘several’), which occur often in ordinary language and in science. LG's provide a framework for distinct notions of ‘generally’: one builds a specific logic for the notion one has in mind. We introduce deductive systems, in sequent calculus style, for LG's and we examine cut elimination.