Analogical proportions are statements of the form ”a” is to ”b” as ”c” is to ”d”.

In the last fifteen years, different formal models of analogical proportions have been proposed in various settings including sets, lattices, trees, etc.

A logical modeling of analogical proportions has been proposed in the Boolean setting, and extended to multiple-valued logics.

An analogical proportion then states that “a differs from b as c differs from d” and vice-versa. It is thus a matter of dissimilarity as much as similarity.

Analogical proportions provide a symbolic counterpart to numerical proportions. They transpose the “rule of three” to symbolic items,

allowing to induce a 4th item when only the 3 others are known. This is the core of analogical-based learning methods.

Its interest relies on the “creative” nature of the process which looks at similar items (as in the neighborhood-based methods),

but takes also advantage of dissimilar, but “parallel” cases. The aim of the talk is to provide the audience with an introduction

to the logical modeling of analogical proportions and their use in classification tasks. Other related logical proportions of interest will be also mentioned.

The work presented has been developed in joint works with Laurent Miclet, Gilles Richard, and more recently Myriam Bounhas.

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## Machine Learning Methods e-session

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