🤖 AI Summary
This paper addresses the asymptotic modeling problem of aggregation functions and Mostowski-type generalized quantifiers in [0,1]-valued logic. Methodologically, it introduces a general asymptotic elimination framework, centered on the first formalization of “local continuity” — defined via a dual-path characterization — which yields a necessary and sufficient condition for asymptotic eliminability of aggregation functions. The approach integrates continuous logic, aggregation function theory, generalized quantifier semantics, asymptotic analysis, and model theory. The main contribution is proving that every locally continuous aggregation function is asymptotically eliminable, thereby uniformly capturing classical generalized quantifiers such as *most*, *many*, and *almost all*. This result transcends established expressivity boundaries in fuzzy and computable logics concerning quantification, and provides a novel pathway toward simplifying quantificational structure and advancing decidability analysis in logical systems.
📝 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.
