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Journal of Logic and Computation Advance Access originally published online on August 6, 2007
Journal of Logic and Computation 2007 17(4):727-747; doi:10.1093/logcom/exm020
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Two Representation Theorems for Non-monotonic Inference Relations*

Zhaohui Zhu

Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing, P. R. China, 210016 and State Key Lab of Novel Software Technology, Nanjing University Nanjing, P. R. China, 210093 E-mail: bnj4892856{at}jlonline.com; Zhaohui{at}nuaa.edu.cn

Wenjie Xiao

Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing, P. R. China, 210016 E-mail: Xiaowj_1981{at}hotmail.com

Received 7 August 2006.


  Abstract

This article considers some semantical properties of the postulates Weak Determinacy (WD) and Rational Contraposition (RC). In particular, we provide two representation theorems for preferential inference relations satisfying WD and RC respectively. This solves two open problems presented by H.Bezzazi, D.Makinson and R.Pino Pérez in [Journal of Logic and Computation, 7, 1997].

Keywords: Non-monotonic logic; preferential models; weak determinacy; rational contraposition; representation theorem

*This work received financial support of the National Natural Science of China (No. 60496327, 60573070), the NSF of Jiangsu Province and Fok Ying Tong Education Foundation.


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