Non-monotonic Logic Based on the Certainty of the Inferred Knowledge Information and Its Applications

点击翻译按钮获取中文摘要

The results of the project are summarized in the following three points :(1) Default Logic proposed by Reiter, Non-monotonic Logic proposed by McDermott and Doyle, Autoepistemic Logic proposed by Moore and Conditional Default Logic proposed by Delgrande are suitable for incomplete knowledge reasoning in artificial intelligence, logic programming and deductive database, because these logics can draw plausible conclusions from the incomplete axioms. Since the conclusions can be invalidated when the partial world description is supplemented by new information, these logics are generally called "nonmonotonic logic". In these logics, however, since the incomplete knowledges interact with each other or with first order formulae (complete knowledges), the sets of beliefs derivable from the logics sometimes contain counterintuitive results. From a theoretical analysis, we discuss the relation between the set of inferred beliefs and the method of knowledge representation and use of these logics … More . We conclude that Reiter's Default Logic is the most significant logic and it should be investigated in more detail.(2) A certainty measure of the beliefs inferred by Reiter's Default Logic is proposed, and its properties are discussed. The measure is introduced by the assumption that the more the number of default rules are applied, the more the inferred result becomes uncertain. By using the measure, we propose a new non-monotonic logic in which the set of inferred beliefs possess some certainty order. In this logic, since we can chose a set of beliefs with appropriate certainty for each purpose, the counterintuitive results deduced in Reiter' s Default Logic can be nicely disposed. If a set of inferred beliefs with infinite certainty order exists, the set is identical with the Reiter's one. Besides the property, many interesting properties about the logic are given.(3) We realize the proposed non-monotonic logic in a small experimental expert system. The system is constructed by Prolog. The experimental results confirm us that the proposed non-monotonic logic gives more intuitive deduction results. Less