Fuzzy Quantifiers

From a linguistic perspective, it is quanti?cation which makes all the di?- ence between having no dollars and having a lot of dollars. And it is the meaning of the quanti?er most which eventually decides if Most Ame- cans voted Kerry or Most Americans voted Bush (as it stands). Natural language(NL)quanti?erslikeall,almostall,manyetc. serveanimp- tant purpose because they permit us to speak about properties of collections, as opposed to describing speci?c individuals only; in technical terms, qu- ti?ers are a 'second-order' construct. Thus the quantifying statement Most Americans voted Bush asserts that the set of voters of George W. Bush c- prisesthemajorityofAmericans,whileBushsneezesonlytellsussomething about a speci?c individual. By describing collections rather than individuals, quanti?ers extend the expressive power of natural languages far beyond that of propositional logic and make them a universal communication medium. Hence language heavily depends on quantifying constructions. These often involve fuzzy concepts like tall, and they frequently refer to fuzzy quantities in agreement like about ten, almost all, many etc. In order to exploit this expressive power and make fuzzy quanti?cation available to technical applications, a number of proposals have been made how to model fuzzy quanti?ers in the framework of fuzzy set theory. These approaches usually reduce fuzzy quanti?cation to a comparison of scalar or fuzzy cardinalities [197, 132].

First monograph on fuzzy quantification Strong emphasis on linguistic justification and formal soundness of interpretations

Autorentext

Ingo Glöckner received his M.A. in Computational Linguistics and Artificial Intelligence from University of Osnabrück in 1996. He then became a research assistant at the University of Bielefeld, where he pursued research on fuzzy set theory and its application to information retrieval. In 2003, I. Glöckner received his PhD for his thesis on the semantical interpretation and implementation of fuzzy quantifiers. He then joined the Intelligent Information and Communication Systems Group (Prakt. Informatik VII) of Prof. H. Helbig at the FernUniversität in Hagen. His current research activities are centered on the representation and processing of knowledge expressed in natural language.

Klappentext

"Almost all", "many", "some": fuzzy quantifiers are vital for effective communication in natural language (NL). This monograph pursues an axiomatic method to achieve a reliable interpretation of these quantifiers in technical applications of fuzzy quantification. Unlike existing work in this area, it targets a much broader class of quantificational phenomena which includes all cases usually considered in linguistics. The topics addressed in the monograph run the gamut from the introduction of the theoretical framework for analysing fuzzy quantification, the formalization of semantical requirements on models of fuzzy quantification, the construction and detailed study of prototypical models which conform to the linguistic desiderata, the development of algorithms for implementing the main types of quantifiers in these models, and finally a preview to fuzzy branching quantifications which might be necessary for modelling NL sentences involving more than one quantifier. The material will be of interest to those working at the crossroads of natural language and fuzzy set theory. The fields of application comprise fuzzy information aggregation and data fusion, flexible database querying and fuzzy information retrieval, multi-criteria decision-making and linguistic data summarization.

Inhalt
An Introduction to Fuzzy Quantification: Origins and Basic Concepts.- A Framework for Fuzzy Quantification.- The Axiomatic Class of Plausible Models.- Semantic Properties of the Models.- Special Subclasses of Models.- Special Semantical Properties and Theoretical Limits.- Models Defined in Terms of Three-Valued Cuts and Fuzzy-Median Aggregation.- Models Defined in Terms of Upper and Lower Bounds on Three-Valued Cuts.- The Full Class of Models Defined in Terms of Three-Valued Cuts.- The Class of Models Based on the Extension Principle.- Implementation of Quantifiers in the Models.- Multiple Variable Binding and Branching Quantification.- Discussion.