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

2023/04/16 by Koponen, Vera, Weitkämper, Felix
#03B50 #03C10 #03C80 #F.4.1 #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #O3C13

paper · doi:10.48550/arxiv.2304.07865

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.

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