A general approach to asymptotic elimination of aggregation functions and generalized quantifiers

Abstract We consider a logic with truth values in the unit interval and which uses aggregation functions instead of quantifiers, and we describe a general approach to asymptotic elimination of aggregation functions and, indirectly, of asymptotic elimination of Mostowski style generalized quantifiers, since such can be expressed by using aggregation functions. The notion of “local continuity” of an aggregation function, which we make precise in two (related) ways, plays a central role in this approach.