Knowledge Reuse for Open Constraint-Based Inference

Open constraint programming, including open constraint satisfaction (Open COP) and open constraint optimization (Open COP), is an extended constraint programming framework designed to model and solve practical problems with openworld settings. We extend open constraint programming to the Open Constraint-Based Inference (Open CBI) framework based on the unified semiring-based CBI framework. The Open CBI framework subsumes both Open CSP and Open COP and also provides extensibility to cover more application domains. Furthermore, the Open CBI framework relaxes the assumption of domain value being incrementally discovered and revealed in non-decreasing order of cost, as required in open constraint programming. We have shown that junction tree representations and junction tree algorithms can be applied to handle Open CBI problems. We show in this paper that the junction tree representation is a suitable graphical model to reuse the intermediate computational results to subproblems. We also proposed consistency maintenance algorithms for junction tree to Open CBI problems with domain value addition and removal. We analyze and show that both answering the satisfiability or the optimal weight of the problem and finding total assignment of variables can be achieved in time that is linear in the size of the junction tree, which is fractionally smaller than the time needed to enforce the junction tree consistency from scratch. We also discuss directions of future research in applying graphical models to problems with open-world settings.