Logical definition of analogical proportion and its fuzzy extensions

Miclet, L; Prade, H

Logical definition of analogical proportion and its fuzzy extensions

Miclet, L Prade, H

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Publication Type:: Conference Proceeding
Citation:: Annual Conference of the North American Fuzzy Information Processing Society - NAFIPS, 2008
Issue Date:: 2008-09-11

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Field	Value	Language
dc.contributor.author	Miclet, L	en_US
dc.contributor.author	Prade, H https://orcid.org/0000-0003-4586-8527	en_US
dc.date.issued	2008-09-11	en_US
dc.identifier.citation	Annual Conference of the North American Fuzzy Information Processing Society - NAFIPS, 2008	en_US
dc.identifier.isbn	9781424423521	en_US
dc.identifier.uri	http://hdl.handle.net/10453/32871
dc.description.abstract	An analogical proportion is a statement of the form "A is to B as C is to D". In a logical setting, items A, B, C and D are Boolean vectors. This notion is at the core of analogical reasoning. This paper proposes a sound definition of analogical proportion, based on a logical expression that holds true for each vector component if and only if the analogical proportion holds true. The analogical equation, where D is unknown, is also discussed. The logical expression of the analogical proportion has several equivalent forms, which may lead to distinct extensions when the vector components takes its values in the unit interval, depending on the choice of the multiple-valued connectives. Applications to case-based and approximate reasoning, and to learning are outlined. ©2008 IEEE.	en_US
dc.relation.ispartof	Annual Conference of the North American Fuzzy Information Processing Society - NAFIPS	en_US
dc.relation.isbasedon	10.1109/NAFIPS.2008.4531257	en_US
dc.title	Logical definition of analogical proportion and its fuzzy extensions	en_US
dc.type	Conference Proceeding
utslib.for	0801 Artificial Intelligence and Image Processing	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

Abstract:

An analogical proportion is a statement of the form "A is to B as C is to D". In a logical setting, items A, B, C and D are Boolean vectors. This notion is at the core of analogical reasoning. This paper proposes a sound definition of analogical proportion, based on a logical expression that holds true for each vector component if and only if the analogical proportion holds true. The analogical equation, where D is unknown, is also discussed. The logical expression of the analogical proportion has several equivalent forms, which may lead to distinct extensions when the vector components takes its values in the unit interval, depending on the choice of the multiple-valued connectives. Applications to case-based and approximate reasoning, and to learning are outlined. ©2008 IEEE.

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http://hdl.handle.net/10453/32871