The Geometry of Meaning

by Widdows

• ISBN13: 9781575864488
• ISBN10: 1575864487
• Format: Paperback
• Copyright: 2004-11-15
• Publisher: Stanford Univ Center for the Study

Summary

From Pythagoras's harmonic sequence to Einstein's theory of relativity, geometric models of position, proximity, ratio, and the underlying properties of physical space have provided us with powerful ideas and accurate scientific tools. Currently, similar geometric models are being applied to another type of space--the conceptual space of information and meaning, where the contributions of Pythagoras and Einstein are a part of the landscape itself. The rich geometry of conceptual space can be glimpsed, for instance, in internet documents: while the documents themselves define a structure of visual layouts and point-to-point links, search engines create an additional structure by matching keywords to nearby documents in a spatial arrangement of content. What the Geometry of Meaning provides is a much-needed exploration of computational techniques to represent meaning and of the conceptual spaces on which these representations are founded.

Table of Contents

Geometry, numbers and sets	p. 1
The graph model : networks of concepts	p. 41
The vertical direction : concept hierarchies	p. 68
Measuring similarity and distance	p. 98
Word-vectors and search engines	p. 132
Exploring vector spaces in one and more languages	p. 167
Logic with vectors : ambiguous words and quantum states	p. 200
Concept lattices : binding everything loosely together	p. 246
Conclusions and curtain call	p. 289
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