On Ultrafilter Logic and Special Functions

Studia Logica 78 (3):459-477 (2004)
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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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References found in this work

Mathematical logic.Joseph R. Shoenfield - 1967 - Reading, Mass.,: Addison-Wesley.
Model-Theoretic Logics.Jon Barwise & Solomon Feferman - 2017 - Cambridge University Press.
Fuzzy logic and approximate reasoning.L. A. Zadeh - 1975 - Synthese 30 (3-4):407-428.
A logic for default reasoning.Ray Reiter - 1980 - Artificial Intelligence 13 (1-2):81-137.

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