Looking for analogical proportions in a formal concept analysis setting

Abstract

Categorization and analogical reasoning are two important cognitive processes, for which there exist formal counterparts (at least they may be regarded as such): namely, formal concept analysis on the one hand, and analogical proportions (modeled in propositional logic) on the other hand. This is a first attempt aiming at relating these two settings. The paper presents an algorithm that takes advantage of the lattice structure of the set of formal concepts for searching for analogical proportions that may hold in a formal context. Moreover, properties linking analogical proportions and formal concepts are laid bare.