Therapy Plans as Hierarchically Structured Graphs

The paper deals with fundamentals of therapy planning in complex dynamic technological systems. Therapy plans (plans, for short) are introduced via several concepts of hierarchical graph structures. There are investigated hierarchically structured families of plans as collections of pin graphs, rooted families of plans, hierarchically structured plans, and plans itself. Emphasis is put on the integration of graph-theoretic concepts and AI applications. Knowledge-based supervision and control is investigated for a class of particularly complex dynamic processes. Therapy of malfunctions turns out to be diicult and needs suuciently exible and expressive planning concepts. These are the graph-theoretic concepts investigated. The approach allows to carefully distinguish between plans to be executed and plans to be revised. It provides the formal background for correctness and completeness concepts of certain planners. Based on this theoretical background, a prototypical planner has been implemented and tested. In fact, this planner accomplishs inductive program synthesis. This paper is intended to provide the formal concepts underlying our approach towards therapy plan generation for complex dynamic systems as outlined in Arn92]. It is particularly aimed at explaining the use of graph-theoretic concepts for applications in artiicial intelligence 1. There is a couple of variants of a planning algorithm (cf. AJ95]) based on this approach. In their right perspective, these algorithms accomplish inductive program synthesis (cf. AJ94a]). We feel the urgent need for clear notions and notations opposed to statements like \A plan in ILP 2 is taken to be a set of assumptions about the future." in Pel91], p. 132. This seems not only vague, but quite useless. In particular, deeper questions like the one whether or not a certain plan is always a sequentially structured object need some formal basis for consideration. In our application, plans are assembled upon a collection of action scripts. Those action scripts are chosen from some complex hierarchical technology representation, where elementary or compound action scripts are attached to technological objects. They represent control knowledge within the Joint Project (BMFT-Verbundprojekt) Wiscon on Development of Methods for Intelligent Monitoring and Control under contract no. 413-4001-01 IW 204 B. 1 According to a referee's request, we have reduced the investigation of graph-theoretic concepts to gain more space for illustrating the application in plan generation. This seems more appropriate for the expected audience at