Tranformation of cost-based hypothetical reasoning into two continuous optimization problems and a reasoning method with their collaboration

Cost-based Hypothetical Reasoning is an important framework for knowledge-based systems; however it is a form of non-monotonic reasoning and thus an NP-hard problem. To find a near-optimal solution in polynomial time with respect to problem size, some algorithms have been developed so far using optimization techniques. In this paper, we show two major ways of transforming prepositional clauses in the hypothetical reasoning problems into constraints. One transforms the clauses into linear inequalities and is good at getting a low-cost solution, while the other transforms them into non-linear equalities and is good at finding a feasible solution. We them show a method of integrating these two transformations by using augmented Lagrangian method. Here, each variable and constraint is regarded as a processor and the searh is realized by their interaction. Two kinds of processors are derived from the two transformations; the structure of these processors are changed dynamically during the search. The cooperation of these two processors allows to obtain better near-optimal solutions than by our previous SL method. This effect is shown in the experiments using two problems with different problem structures.