DFS - An Axiomatic Approach to Fuzzy Quantification

Abstract

Fuzzy quantifiers (like many, few,...) are an important research topic not only due to their abundance in natural language, but also because an adequate account of these quantifiers would provide a class of powerful yet human-understandable operators for information aggregation. In the report, we present an axiomatic approach to fuzzy quantification which builds on the novel concept of a Determiner Fuzzification Scheme (or DFS for short). DFS theory overcomes several limitations pertinent to the approaches to fuzzy quantification described in the literature. Unlike these approaches, DFS is

• a compatible extension of the Theory of Generalized Quantifiers [Barwise&Cooper81,vanBenthem 83];
• a genuine theory of fuzzy multi-place quantification;
• not limited to absolute and proportional quantifiers;
• not limited to automorphism-invariant quantifiers;
• not limited to finite universes of discourse;
• based on a rigid axiomatic foundation ensuring important formal properties;
• fully compatible to the formation of negation, antonyms, and duals.

Due to the axiomatic rigor of its foundation, its nice theoretical properties, its broad coverage of quantificational phenomena, and the existence of computational models, DFS theory not only contributes to a better understanding of fuzzy quantification in general, but also allows for a principled account of fuzzy quantifiers in practical applications.

Reference

I. Glöckner
DFS: An Axiomatic Approach to Fuzzy Quantification
Technical Report TR97-06, Technische Fakultät, Universität Bielefeld, 1997

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