DFS - An Axiomatic Approach to Fuzzy Quantification

Fuzzy quantifiers (likemany, few, : : : ) are an important research topic not only due to their abundance in natural language, but also because an adequate acco unt of these quantifiers would provide a class of powerful yet human-understandable operators for in mation aggregation. In the report, we present an axiomatic approach to fuzzy quantificati on which builds on the novel concept of a Determiner Fuzzification Scheme (or DFS for short). DFS t heory overcomes several limitations pertinent to the approaches to fuzzy quantification de scribed in the literature. Unlike these approaches, DFS is a compatible extension of the Theory of Generalized Quantifi ers [12, 13]; 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 fo rmal properties; fully compatible to the formation of negation, antonyms, an d duals. Due to the axiomatic rigor of its foundation, its nice theore tical properties, its broad coverage of quantificational phenomena, and the existence of computati onal models, DFS theory not only contributes to a better understanding of fuzzy quantification i n general, but also allows for a principled account of fuzzy quantifiers in practical applications. 1 1Parts of the work reported here were funded by the ministry of science and research of the state of NorthrhineWestphalia within the collaborative research initiative “ Virtual Knowledge Factory”.