Proportional Analogy in Written Language Data

Abstract

The purpose of this paper is to summarize some of the results obtained over many years of research in proportional analogy applied to natural language processing. We recall some mathematical formalizations obtained based on general axioms drawn from a study of the history of the notion from Euclid to modern linguistics. The obtained formalization relies on two articulative notions: conformity and ratio, and on two constitutive notions: similarity and contiguity. These notions are applied on a series of objects that range from sets to strings of symbols through multi-sets and vectors, so as to obtain a mathematical formalization on each of these types of objects. Thanks to these formalizations, some results are presented that were obtained in structuring language data by the characters (bitmaps), words or short sentences in several languages like Chinese or English. An important point in using such formalizations that rely on form only, concerns the truth of the analogies retrieved or produced, i.e., whether they are valid on both the levels of form and meaning. Results of evaluation on this aspect are recalled. It is also mentioned how the formalization on string of symbols can be applied to two main tasks that would correspond to ‘langage’ and ‘parole’ in Saussurian terms: structuring language data and generating language data. The results presented have been obtained from reasonably large amounts of language data, like several thousands of Chinese characters or hundred thousand sentences in English or other languages.