Evaluation of analogical proportions through Kolmogorov complexity

Bayoudh, M; Prade, H; Richard, G

Evaluation of analogical proportions through Kolmogorov complexity

Bayoudh, M Prade, H

Richard, G

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Publication Type:: Journal Article
Citation:: Knowledge-Based Systems, 2012, 29 pp. 20 - 30
Issue Date:: 2012-05-01

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Field	Value	Language
dc.contributor.author	Bayoudh, M	en_US
dc.contributor.author	Prade, H https://orcid.org/0000-0003-4586-8527	en_US
dc.contributor.author	Richard, G	en_US
dc.date.issued	2012-05-01	en_US
dc.identifier.citation	Knowledge-Based Systems, 2012, 29 pp. 20 - 30	en_US
dc.identifier.issn	0950-7051	en_US
dc.identifier.uri	http://hdl.handle.net/10453/32399
dc.description.abstract	In this paper, we try to identify analogical proportions, i.e., statements of the form "a is to b as c is to d", expressed in linguistic terms. While it is conceivable to use an algebraic model for testing proportions such as "2 is to 4 as 5 is to 10", or even such as "read is to reader as lecture is to lecturer", there is no algebraic framework to support statements such as "engine is to car as heart is to human" or "wine is to France as beer is to England", helping to recognize them as meaningful analogical proportions. The idea is then to rely on text corpora, or even on the Web itself, where one may expect to find the pragmatics and the semantics of the words, in their common use. In that context, in order to attach a numerical value to the "analogical ratio" corresponding to the phrase "a is to b", we start from the works of Kolmogorov on complexity theory. This is the basis for a universal measure of the information content of a word a, or of a word a with respect to another one b, which, in practice, is estimated in a statistical manner. We investigate the link between a purely logical, recently introduced view of analogical proportions and its counterpart based on Kolmogorov theory. The criteria proposed for testing candidate proportions fit with the expected properties (symmetry, central permutation) of analogical proportions. This leads to a new computational method to define, and ultimately to try to detect, analogical proportions in natural language. Experiments with classifiers based on these ideas are reported, and results are rather encouraging with respect to the recognition of common sense linguistic analogies. The approach is also compared with existing works on similar problems. © 2011 Elsevier B.V. All rights reserved.	en_US
dc.relation.ispartof	Knowledge-Based Systems	en_US
dc.relation.isbasedon	10.1016/j.knosys.2011.06.022	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	Evaluation of analogical proportions through Kolmogorov complexity	en_US
dc.type	Journal Article
utslib.citation.volume	29	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
utslib.for	08 Information and Computing Sciences	en_US
utslib.for	15 Commerce, Management, Tourism and Services	en_US
utslib.for	17 Psychology and Cognitive Sciences	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Software
pubs.organisational-group	/University of Technology Sydney/Strength - CAI - Centre for Artificial Intelligence
utslib.copyright.status	closed_access
pubs.publication-status	Published	en_US
pubs.volume	29	en_US

Abstract:

In this paper, we try to identify analogical proportions, i.e., statements of the form "a is to b as c is to d", expressed in linguistic terms. While it is conceivable to use an algebraic model for testing proportions such as "2 is to 4 as 5 is to 10", or even such as "read is to reader as lecture is to lecturer", there is no algebraic framework to support statements such as "engine is to car as heart is to human" or "wine is to France as beer is to England", helping to recognize them as meaningful analogical proportions. The idea is then to rely on text corpora, or even on the Web itself, where one may expect to find the pragmatics and the semantics of the words, in their common use. In that context, in order to attach a numerical value to the "analogical ratio" corresponding to the phrase "a is to b", we start from the works of Kolmogorov on complexity theory. This is the basis for a universal measure of the information content of a word a, or of a word a with respect to another one b, which, in practice, is estimated in a statistical manner. We investigate the link between a purely logical, recently introduced view of analogical proportions and its counterpart based on Kolmogorov theory. The criteria proposed for testing candidate proportions fit with the expected properties (symmetry, central permutation) of analogical proportions. This leads to a new computational method to define, and ultimately to try to detect, analogical proportions in natural language. Experiments with classifiers based on these ideas are reported, and results are rather encouraging with respect to the recognition of common sense linguistic analogies. The approach is also compared with existing works on similar problems. © 2011 Elsevier B.V. All rights reserved.

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http://hdl.handle.net/10453/32399