Analogical Proportions: Why They Are Useful in AI

This paper presents a survey of researches in analogical reasoning whose building block are analogical proportions which are statements of the form “a is to b as c is to d”. They have been developed in the last twenty years within an Artificial Intelligence perspective. After discussing their formal modeling with the associated inference mechanism, the paper reports the main results obtained in various AI domains ranging from computational linguistics to classification, including image processing, I.Q. tests, case based reasoning, preference learning, and formal concepts analysis. The last section discusses some new theoretical concerns, and the potential of analogical proportions in other areas such as argumentation, transfer learning, and XAI.