On Ultrafilter Logic and Special Functions

Studia Logica 78 (3):459-477 (2004)

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.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1007/s11225-004-6045-y
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Mathematical Logic.Joseph R. Shoenfield - 1967 - Reading, Mass., Addison-Wesley Pub. Co..
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