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On Ultrafilter Logic and Special Functions

Paulo A. S. Veloso and Sheila R. M. Veloso
Studia Logica: An International Journal for Symbolic Logic
Vol. 78, No. 3 (Dec., 2004), pp. 459-477
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016668
Page Count: 19
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On Ultrafilter Logic and Special Functions
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Abstract

Logics for 'generally' were introduced for handling assertions with vague notions, such as 'generally', 'most', 'several', etc., by generalized quantifiers, ultrafilter logic being an interesting case. Here, we show that ultrafilter logic can be faithfully embedded into a first-order theory of certain functions, called coherent. We also use generic functions (akin to Skolem functions) to enable elimination of the generalized quantifier. These devices permit using methods for classical first-order logic to reason about consequence in ultrafilter logic.

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