Evenness-Based Reasoning with Logical Proportions Applied to Classification

  • Myriam BounhasEmail author
  • Henri Prade
  • Gilles Richard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9310)


An approach to classification, based on a formal modeling of analogical proportions linking the features of 4 items, has been recently shown to be surprisingly successful on difficult benchmarks. Analogical proportions are homogeneous logical proportions. Homogeneous here refers both to the structure of their logical expression and to the specificity of their truth tables. In contrast, heterogeneous proportions express that there is an intruder among 4 truth values, which is forbidden to appear in a specific position. The 2 types of proportions are of an opposite nature. However heterogeneous proportions can also be considered as a basis for classification by considering that a new item can be added to a class only if its addition leaves the class as even as possible: the new item should rarely be an intruder with respect to any triple of items known to be in the class. Experiments show that this new evenness-based classifier gets good results on a number of representative benchmarks. Its accuracy is both compared to the ones of well-known classifiers and to previous analogy-based classifiers. A discussion investigates on what type of particular benchmarks the evenness-based classifiers outperform the analogical ones and when it is the opposite.


Logical Proportions Heterogeneous Proportions Proportional Analogy Evenness-based Classifiers Truth Table 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LARODEC LaboratoryISG de TunisLe BardoTunisia
  2. 2.Emirates College of TechnologyAbu DhabiUAE
  3. 3.IRITUniversity of ToulouseToulouseFrance
  4. 4.QCISUniversity of TechnologySydneyAustralia

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