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March 2002 Valuation structure
Shifu Chen, Zhenghua Pan, Zhaohui Zhu, Wujia Zhu
J. Symbolic Logic 67(1): 1-23 (March 2002). DOI: 10.2178/jsl/1190150026

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.

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Shifu Chen. Zhenghua Pan. Zhaohui Zhu. Wujia Zhu. "Valuation structure." J. Symbolic Logic 67 (1) 1 - 23, March 2002. https://doi.org/10.2178/jsl/1190150026

Information

Published: March 2002
First available in Project Euclid: 18 September 2007

zbMATH: 1002.03020
MathSciNet: MR1889533
Digital Object Identifier: 10.2178/jsl/1190150026

Subjects:
Primary: 03B60
Secondary: 68T27

Rights: Copyright © 2002 Association for Symbolic Logic

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Vol.67 • No. 1 • March 2002
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