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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月25日

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  • Vera Koponen,
  • Felix Weitkämper

摘要

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.