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Valuation structure

Published online by Cambridge University Press:  12 March 2014

Zhaohui Zhu ,
Zhenghua Pan ,
Shifu Chen  and
Wujia Zhu
Zhaohui Zhu
Affiliation:
Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing, China210016 State Key Lab of Novel Software Technology, Nanjing University, Nanjing, China210093, E-mail: [email protected]
Zhenghua Pan
Affiliation:
Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing, China210016, E-mail: [email protected]
Shifu Chen
Affiliation:
State Key Lab of Novel Software Technology, Nanjing University, Nanjing, China210093, E-mail: [email protected]
Wujia Zhu
Affiliation:
State Key Lab of Novel Software Technology, Nanjing University, Nanjing, China210093 Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing, China210016, E-mail: [email protected]
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Abstract

This paper introduces valuation structures associated with preferential models. Based on KLM valuation structures, we present a canonical approach to obtain injective preferential models for any preferential relation satisfying the property INJ, and give uniform proofs of representation theorems for injective preferential relations appeared in the literature. In particular, we show that, in any propositional language (finite or infinite), a preferential inference relation satisfies INJ if and only if it can be represented by a standard preferential model. This conclusion generalizes the result obtained by Freund. In addition, we prove that, when the language is finite, our framework is sufficient to establish a representation theorem for any injective relation.

Keywords

nonmonotonic logicinjective inference relationvaluation structurerepresentation theoremINJ property
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 1 , March 2002 , pp. 1 - 23
Copyright
Copyright © Association for Symbolic Logic 2002

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References

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