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

（1）Reiter提出的缺省逻辑、McDermott和Doyle提出的非单调逻辑、摩尔提出的自认知逻辑和Delaware提出的条件缺省逻辑，由于能从不完备公理中得出似然结论，因此适用于人工智能、逻辑程序设计和演绎数据库中的不完备知识推理。由于当部分世界描述被新信息补充时，结论会失效，因此这些逻辑通常被称为“非单调逻辑”。然而，在这些逻辑中，由于不完整的知识彼此相互作用或与一阶公式（完整的知识）相互作用，从逻辑中导出的信念集有时包含违反直觉的结果。从理论上分析了推理信念集与知识表示方法的关系以及推理信念逻辑的使用 ...更多信息 .我们的结论是，赖特的默认逻辑是最重要的逻辑，它应该得到更详细的研究。(2)提出了一种由Reiter的缺省逻辑推理出的信念的确定性测度，并讨论了它的性质。该度量是通过假设应用的默认规则的数量越多，推断的结果变得越不确定来引入的。利用这个测度，我们提出了一个新的非单调逻辑，其中的推断信念集具有一定的确定性顺序。在这种逻辑中，由于我们可以为每个目的选择一组具有适当确定性的信念，因此可以很好地处理赖特缺省逻辑中推导出的违反直觉的结果。如果存在一个具有无限确定性次序的推断信念集合，则该集合与Reiter的集合相同。除此之外，还给出了关于该逻辑的许多有趣的性质。(3)我们实现了一个小型的实验专家系统中提出的非单调逻辑。该系统是用Prolog语言构建的。实验结果表明，所提出的非单调逻辑给出了更直观的推理结果。少

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