Some recent advances in reasoning based on analogical proportions

Analogical proportions (AP) are statements of the form "a is to b ascis to d". They compare the pairs of items(a,b) and(c, d) in terms of their differences and similarities. The explicit use of APs in analogical reasoning has contributed to a renewal of its applications, leading to many developments, especially in the last decade; see [30] for a survey. However, even if much has been already done both at the theoretical and at the practical levels, the very nature of APs may not yet be fully understood and their full potential explored. In the following, we survey recent works on APs along three directions: their role in classification tasks [4]; their use for providing explanations [20]; their relation with multi-valued dependencies [21]. This just intends to be an introductory paper, and the reader is referred to the above references for more details on each issue.