A Study of Hypothetical Reasoning Using Lagrangian Method

Abstract

Hypothetical reasoning is one of important reasoning frameworks because of its usefulness for some practical problems such as diagnosis,design,etc. Given a set of observations, hypothetical reasoning is an abductive reasoning mechanism to find consistent hypotheses. We consider cost-based hypothetical reasoning. Cost-based hypothetical reasoning associates a cost with each hypothesis, then the best explanation is defined as an explanation which has the least sum of the cost corresponding to each hypothesis. We have proposed the Lagrange programming neural network with polarized high-order connections (LPPH) as an effective technique for satisfiability problem (SAT). In this paper, at first we describe a method to accomplish deductive reasoning approximately using LPPH with bias. Then, we discuss cost-based hypothetical reasoning with restrictive background knowledge. One of the restrictions used is that background knowledge is represented by prepositional horn clauses