A general framework for shape similarity

We propose a formal framework to clarify the import of and the relationship among different notions of similarity. The framework, borrowing from the general E-connections approach, allows to use multiple similarity notions in the same system by relating the domain of discourse to specialized sets of entities even across different logics. In practice, we start form the assumption that (Leibnizian) relative identity is the only local form of similarity, and show that more sophisticated notions can be conceptually understood as the result of transformations across heterogeneous logics. These transformations, called global similarities, are usually motivated by arguments external to the starting system, and can be intertwined to generate a prolific family of similarity relations. We exemplify this framework in the context of shape similarity whose comprehension motivated our work. Finally, the approach developed in this paper sets the basis for a general study of similarity as a group of transformations generated by (primitive) global similarity relations.