HAN Qing, LIN Zuo-Quan

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HAN Qing, LIN Zuo-Quan,  (Department of Information Science, Peking University, Beijing 100871, China)
Authors information: HAN Qing was born in 1976. He is a Ph.D. candidate at Department of Information Science, Peking University. His current research interests include knowledge representation and reasoning. LIN Zuo-Quan was born in 1963. He is a professor at Department of Information Science, Peking University. His research areas are computer science and artificial intelligence.
Corresponding author: LIN Zuo-Quan, Phn: +86-10-62757175, E-mail: lz@is.pku.edu.cn, http://www.is.pku.edu.cn
Received 2003-12-26; Accepted 2004-03-17

Abstract
A novel theory called bi-default theory is proposed for handling inconsistent knowledge simultaneously in the context of default logic without leading to triviality of the extension. To this end, the positive and negative transformations of propositional formulas are defined such that the semantic link between a literal and its negation is split. Most theorems of default logic can be reproduced in the setting of the bi-default logic. It is proven that the bi-default logic is a generalization of the default logic in the presence of inconsistency. A method is provided as an alternative approach for making the reasoning ability of paraconsistent logic as powerful as the classical one.

Han Q, Lin ZQ. Default reasoning with inconsistent knowledge. Journal of Software, 2004,15(7):1030~1041.
http://www.jos.org.cn/1000-9825/15/1030.htm


摘要
提出了一个新的缺省推理理论,称为双缺省理论,使得缺省逻辑在四值语义下能够同时处理不协调的知识而不导致扩张的平凡性.为此,定义了命题公式的正变换和负变换,以便分离一个文字与其否定的语义联系.大多数关于缺省逻辑的定理都可以在双缺省逻辑下重建,证明了双缺省逻辑是缺省逻辑在不协调情形下的一般化.提供了一种方法使得超协调逻辑能够获得类似经典逻辑的推理能力.

基金项目：Supported by the National Natural Science Foundation of China under Grant Nos.69925203, 60373002 (国家自然科学基金)


References: 

[1] Reiter R. A logic for default reasoning. Artificial Intelligence, 1980,13(1-2):81~132.

[2] Hanks S, McDermott D. Nonmonotonic logics and temporal projection. Artificial Intelligence, 1987,33(3):379~412.

[3] Belnap ND. A useful four-valued logic. In: Epstein G, Dunn J M, eds. Modern Uses of Multiple-Valued Logic. Dordrecht: Reidel Publishing Company, 1977. 7~37.

[4] Belnap ND. How computer should think. In: Ryle G, ed. Contemporary Aspects of Philosophy. Stocksfield: Oriel Press, 1977. 30~56.

[5] Kifer M, Lozinskii EL. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 1992,9(2):179~215.

[6] Lin ZQ. Circumscription in a paraconsistent logic. Journal of Software, 1995,6(5):290~295 (in Chinese with English abstract).

[7] Arieli O, Avron A. The value of the four values. Artificial Intelligence, 1998,102(1):97~141.

[8] Ginsberg ML. Multi-Valued logics: A uniform approach to reasoning in AI. Computational Intelligence, 1988,4:256~316.

[9] Priest G. Reasoning about truth. Artificial Intelligence, 1989,39(2):231~244.

[10] Marek W, Treur J, Truszczyński M. Representation theory for default logic. Annals of Mathematics and Artificial Intelligence, 1997,21(2-4):343~358.

[11] Arieli O, Denecker M. Reducing preferential paraconsistent reasoning to classical entailment. Journal of Logic and Computation, 2003,13(4):557~580.

[12] Besnard P, Schaub T. Signed systems for paraconsistent reasoning. Journal of Automated Reasoning, 1998,20(1-2):191~213.

[13] Han Q. A study of nonmonotonic paraconsistent reasoning [Ph.D. Thesis]. Beijing: Peking University, 2004 (in Chinese with English abstract).

[14] Pequeno T, Buchsbaum A. The logic of epistemic inconsistency. In: Allen JA, Fikes R, Sandewall E, eds. Proc. of the 2nd Int'l. Conf. on the Principles of Knowledge Representation and Reasoning. San Mateo: Morgan Kaufmann Publishers, Inc., 1991. 453~560.

附中文参考文献：
[6] 林作铨.一个在弗协调逻辑中的限制.软件学报,1995,6(5):290~295.

[13] 韩庆.非单调超协调推理研究[博士学位论文].北京:北京大学,2004.