Ordering Nonmonotonic Logic Program and its Application to Inductive Learning

一阶理论是在逻辑蕴涵的基础上根据从理论中获得的信息量进行排序的。另一方面，在缺省逻辑中，理论既包含缺省信息，也包含确定信息。要对违约理论进行排序，必须区分不同种类的信息，以评估违约理论的信息内容。为此，我们首先引入了缺省理论的一个多值解释，使用的是一个十值双格。它区分了源自理论的确定的和轻信的/怀疑的违约信息，并用于根据违约理论的信息内容对其进行排序。然后，我们将该技术应用于非单调逻辑程序在答案集语义下的排序。这项研究的结果提供了一种不同于传统的基于扩展/模型的观点来比较缺省理论或非单调逻辑程序的方法。此外，它们在非单调理论的归纳法中有重要的应用。

First-order theories are ordered under logical entailment based on the amount of information derived from theories. In default logic, on the other hand, a theory contains default information as well as definite information. To order default theories, distinguishing different sorts of information is necessary to assess the information content of a default theory. For this purpose, we first introduce a multi-valued interpretation of default theories using a ten-valued bilattice. It distinguishes between definite and credulous/skeptical default information derived from a theory, and is used for ordering default theories based on their information contents. We then apply the technique to order nonmonotonic logic programs under the answer set semantics. The results of this research provide a method for comparing default theories or nonmonotonic logic programs in a manner different from the conventional extension/model-based viewpoint. Moreover, they have important application to induction from nonmonotonic theories.