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理论推导出的信息量进行排序的。另一方面，在缺省逻辑中，一个理论包含缺省信息和确定信息。为了对缺省理论进行排序，区分不同类型的信息对于评估缺省理论的信息含量是必要的。为此，我们首先介绍了一个多值解释的默认理论使用十值双格。它区分来自理论的确定和轻信/怀疑的默认信息，并用于根据其信息内容对默认理论进行排序。然后，我们应用该技术，以回答集语义下的非单调逻辑程序。本研究的结果提供了一种方法比较默认理论或非单调逻辑程序的方式不同于传统的扩展/基于模型的观点。此外，他们有重要的应用，从非单调理论归纳。

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.