Boolean Analogical Proportions - Axiomatics and Algorithmic Complexity Issues

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)

Abstract

Analogical proportions, i.e., statements of the form a is to b as c is to d, are supposed to obey 3 axioms expressing reflexivity, symmetry, and stability under central permutation. These axioms are not enough to determine a single Boolean model, if a minimality condition is not added. After an algebraic discussion of this minimal model and of related expressions, another justification of this model is given in terms of Kolmogorov complexity. It is shown that the 6 Boolean patterns that make an analogical proportion true have a minimal complexity with respect to an expression reflecting the intended meaning of the proportion.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.IRITToulouse UniversityToulouseFrance
  2. 2.QCISUniversity of TechnologySydneyAustralia

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