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Analogical Proportions and Analogical Reasoning - An Introduction

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Case-Based Reasoning Research and Development (ICCBR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10339))

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Abstract

Analogical proportions are statements of the form “a is to b as c is to d”. For more than a decade now, their formalization and use have raised the interest of a number of researchers. In this talk we shall primarily focus on their modeling in logical settings, both in the Boolean and in the multiple-valued cases. This logical view makes clear that analogy is as much a matter of dissimilarity as a matter of similarity. Moreover analogical proportions emerge as being especially remarkable in the framework of logical proportions. The analogical proportion and seven other code independent logical proportions can be shown as being of particular interest. Besides, analogical proportions are at the basis of an inference mechanism which enables us to complete or create a fourth item from three other items. The relation with case-based reasoning and case-based decision is emphasized. Potential applications and current developments are also discussed.

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Notes

  1. 1.

    For copyright reasons and to protect the security of the test problems, the original Raven test has been replaced by an isomorphic example (in terms of logical encoding).

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Authors and Affiliations

  1. IRIT, Toulouse University, Toulouse, France

    Henri Prade & Gilles Richard

  2. QCIS, University of Technology, Sydney, Australia

    Henri Prade

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  1. Henri Prade
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  2. Gilles Richard
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Correspondence to Henri Prade .

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Editors and Affiliations

  1. Naval Research Laboratory, Navy Center for Applied Research in AI, Washington, District of Columbia, USA

    David W. Aha

  2. LORIA/Bâtiment B/équipe Orpailleur, University of Lorraine, Vandœuvre-lès-Nancy Cedex, France

    Jean Lieber

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Prade, H., Richard, G. (2017). Analogical Proportions and Analogical Reasoning - An Introduction. In: Aha, D., Lieber, J. (eds) Case-Based Reasoning Research and Development. ICCBR 2017. Lecture Notes in Computer Science(), vol 10339. Springer, Cham. https://doi.org/10.1007/978-3-319-61030-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-61030-6_2

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