On ‘Most’ and ‘Representative’: Filter Logic and Special Predicates

Logics for ‘generally’ were introduced for handling assertions with vague notions, by non-standard generalized quantifiers, and to reason qualitatively about them (important issues in Logic and in Artificial Intelligence). Filter logic is intended to address (some versions of) ‘most’. Here, we show that filter logic can be faithfully embedded into a classical first-order theory of certain predicates, called compatible. We also use representative predicates to enable elimination of the generalized quantifier. These devices permit using classical first-order methods to reason about consequence in filter logic and help clarifying the role of such extended logics for ‘generally’.