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.