A general approach to asymptotic elimination of aggregation functions and generalized quantifiers
This work provides a theoretical framework for simplifying logical systems by eliminating aggregation functions, relevant to researchers in mathematical logic and fuzzy logic.
The paper presents a general method for asymptotically eliminating aggregation functions in a logic with truth values in [0,1], which also applies to Mostowski-style generalized quantifiers. The key concept is 'local continuity' of aggregation functions, defined in two related ways.
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.