Properties of the $\mathcal{KRA }$ Model

Abstract

In the KRA model approximation and reformulation are never abstractions, but all three are mechanisms aiming in real-world applications at effectively simplifying solving a problem. This chapter provides a definition of abstraction, approximation, and reformulation as well as their relationships with the key notion of information. In our view, abstraction reduces the information, while approximation modifies it, and reformulation leaves it unchanged, only modifying its format. We also explain why and how these three representation changes are used in synergy. Even though the KRA model is primarily thought for a bottom-up use, it can also be used top-down, by inverting the abstraction operators. Another property of abstraction is that it may generate inconsistencies in the abstract space. We show that the only important thing is whether the given problem can or cannot be solved in the abstract space. The unification power of the KRA model concludes this chapter, showing how other models of abstraction nicely fit into it.