A semantics for abstraction

The goal of this paper is to propose a model-theoretic formalization of abstraction, where abstraction is modeled as two representations, the ground and the abstract representation, modeling the same phenomenon at different levels of detali. Using the framework of Local Models Semantics, the gorund and abstract representations are modeled as two sets of (local) first order models, while the relations holding between them are captured by an appropriate `compatibility relation`. The tuning of the compatibility relation allows for the defintion of the many different kinds of abstractio