A Framework for Dynamic Constraint Reasoning Using Procedural Constraints

Many complex real-world decision and control problems contain an underlying constraint reasoning problem. This is particularly evident in a recently developed approach to planning, where almost all planning decisions are represented by constrained variables. This translates a significant part of the planning problem into a constraint network whose consistency determines the validity of the plan candidate. Since higher-level choices about control actions can add or remove variables and constraints, the underlying constraint network is invariably highly dynamic. Arbitrary domain-dependent constraints may be added to the constraint network and the constraint reasoning mechanism must be able to handle such constraints effectively. Additionally, real problems often require handling constraints over continuous variables. These requirements present a number of significant challenges for a constraint reasoning mechanism. In this paper, we introduce a general framework for handling dynamic constraint networks with real-valued variables, by using procedures to represent and effectively reason about general constraints. The framework is based on a sound theoretical foundation, and can be proven to be sound and complete under well-defined conditions. Furthermore, the framework provides hybrid reasoning capabilities, as alternative solution methods like mathematical programming can be incorporated into the framework, in the form of procedures.