Abstraction Operators and Design Patterns

Abstract

This chapter details a fundamental set of abstraction operators, providing a classification thereof, depending on their effects and modus operandi. The classification is based on general properties rather than specific characteristics of the domain of application. Each abstraction operator is described by its name, the issue it addresses and its operationalization in the $\mathcal{KRA }$ formalism. We relate the problem of designing generic operator schemas to the notions of Abstract Procedural Types and Design Patterns, both well known in Software Engineering. These patterns of operators can act as starting point for building new abstractions and may be adapted to specific requirements. In fact, many of the operators correspond to similar representation problems occurring in various domains. Only the most basic operators (hiding, aggregating, composing, building hierarchies,...) is described in detail, in order to provide the reader with the feeling of how operators can be defined in practice and concretely applied. Approximation operators are also introduced and contrasted with abstraction ones. The richness of choices among many kinds of ready-to-use abstraction operators is one of the features that differentiate the $\mathcal{KRA }$ model from previous ones.