A polynomial-time predicate-logic hypothetical reasoning by Networked Bubble Propagation method

Abstract

Hypothetical reasoning is a useful knowledge-processing framework applicable to many problems including system diagnosis, design, etc. However, due to its non-monotonic inference nature, it takes exponential computation-time to find a solution hypotheses-set to prove a given goal. This is also true for cost-based hypothetical reasoning to find an optimal solution with minimal cost. As for the hypothetical reasoning expressed in propositional logic, since it is easily transformed into 0–1 integer programming problem, a polynomial-time method finding a near-optimal solution has been developed so far by employing an approximate solution method of 0–1 integer programming called the Pivot and Complement method. Also, by reforming this method, a network-based inference mechanism called Networked Bubble Propagation (NBP) has been invented by the authors, which allows even faster inference. More importantly, a network-based approach is meaningful, for its potential of being developed extending to a broader framework of knowledge processing. In this paper, we extend the NBP method to dealing with the hypothetical reasoning expressed with predicate logic. By constructing a series of knowledge networks, to which the NBP method is applied, in a stepwise manner according to a top-down control, we avoid the excessive expansion of the network size. As a result, we can achieve a polynomial-time inference for computing a near-optimal solution for the cost-based hypothetical reasoning in predicate-logic knowledge.