Principled Approach to Design of Hierarchical Abstractions

Abstract

The use of hierarchical abstractions allows processing at an abstract level so that the complexity of low-level processing can be avoided or delayed. The idea of hierarchical abstractions is a simple but powerful one in intelligent engineering systems. It is commonly used in a wide range of applications, such as those for design, planning, learning, and natural language processing. It is also ubiquitous in many general paradigms for intelligent systems, such as heuristic search and blackboard architectures. Despite its usefulness and widespread use, the reduction in complexity achieved through hierarchical abstractions has been only informally understood. This can lead to suboptimal designs of hierarchical abstractions. In the present paper, we derive formulas to show how hierarchical abstractions reduce complexity in intelligent engineering systems. Formalizing the costs and benefits of hierarchical abstractions also allows us to see exactly when what kinds of abstractions are useful. We illustrate the practicality of this approach with IPDOS, a system for designing offshore structures. With an improved understanding of the power of hierarchical abstractions, we hope to stimulate even greater use of such abstractions in computing for engineering.