Functional Interpretation of Logics for 'Generally'

Logics for ‘generally’ are intended to express some vague notions, such as ‘generally’, ‘several’, ‘many’, ‘most’, etc., by means of the new generalized quantifier ∇ and to reason about assertions with ‘generally’ (important issues in qualitative reasoning). We introduce the idea of functional interpretation for ‘generally’ and show that representative functions (akin to Skolem functions) enable elimination of ∇ and reduce consequence to classical theories. Thus, one can use proof procedures and theorem provers for classical first-order logic to reason about assertions involving ‘generally’.