A Fast Hypothetical Reasoning System for Predicate-Logic Knowledge-Base

Abstract

Handling incomplete knowledge, involving exception or contradiction, is an important function to expand the capability of current knowledge-base. Hypothetical reasoning handles such incomplete knowledge as hypothesis. It can be directly applicable to model based diagnosis problems, design problems, etc. Thus hypothetical reasoning system is an important framework toward advanced knowledge-based system both from theoretical and practical viewpoints. The most crucial problem of hypothetical reasoning is its slow inference speed due to its non-monotonic reasoning nature. One practical way to overcome this problem is to incorporate such heuristic knowledge that serves to navigate inference-path. But this causes knowledge acquisition bottleneck, because it is difficult to collect all the necessary heuristic knowledge to cover all the problem domain. Therefore, a fast hypothetical reasoning method systematically working under declarative knowledge is indispensable. One key mechanism of efficiency is to combine the advantages of forward reasoning and back-ward one, to reason just once the necessary nodes for proving a goal. This is very effective in hypothetical reasoning, because inefficient backtracking is frequently caused by inconsistency among hypotheses. Meanwhile, variable plays an important role to expand the scope of knowledge representation capability. If we represent knowledge in propositional logic representation without variables, the scale of knowledge-base becomes too large for many practical cases. Using the variables in predicate logic representation, we can express necessary knowledge in a compact form. Thus it is required for a fast hypothetical reasoning system working for predicate-logic knowledge. In this paper we present a fast hypothetical reasoning mechanism for predicate-logic knowledge (actually for function-free predicate Horn-clause knowledge). The QSQR method in deductive data-base technology is effectively applied in the view of dealing with the variables in predicate. The improvement inference speed is shown by some experiments including a practical diagnosis problem of logic circuit.