---
title: "Ordering Default Theories"
authors:
  - "Chiaki Sakama"
doi: ""
url: "https://ijcai.org/proceedings/2003/121"
pdf: "https://ijcai.org/proceedings/2003/0121.pdf"
venue: "Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence"
year: 2003
pages: "839-845"
track: ""
keywords:
---

# Ordering Default Theories

Chiaki Sakama

*Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence*, pages 839-845.

## Abstract

In first-order logic, a theory T 1 is considered stronger than another theory T 2 if every formula derived from T 2 is also derived from T1. Such an order relation is useful to know relative value between different theories. In the context of default logic, a theory contains default information as well as definite information. To order default theories, it is necessary to assess the information content of a default theory. To this end, we introduce a multi-valued interpretation of default theories based on a nine-valued bilattice. It distinguishes definite and credulous/skeptical default information derived from a theory, and is used for ordering default theories based on their information contents. The technique is also applied to order nonmonotonic logic programs. The results of this paper provide a method for comparing different default theories and have important application to learning nonmonotonic theories.