Analogical Learning and Formal Proportions: Definitions and Methodological Issues

Analogical learning is a two-step inference process: (i) computation of a mapping between a new and a memorized situation; (ii) transfer from the known to the unknown situation. This approach requires the ability to search for and exploit such mappings, which are based on the notion of analogical proportions, hence the need to properly define these proportions, and to efficiently implement their computation. In this paper, we propose a unified definition of analogical proportions, which applies to a wide range of algebraic structures. We show that this definition is suitable for learning in domains involving large databases of structured data, as is especially the case of many Natural Language Processing applications. We finally discuss some issues this approach raises and relate it to other instance-based learning schemes.