AbstractThis 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.
摘要本文介绍了与优先模型相关的估值结构。基于KLM估值结构,我们提出了一种规范方法,用于获得任何满足INJ属性的注射式优先模型,并给出了文献中出现的注射式优先关系的统一证明。特别地,我们证明,在任何命题语言(有限或无限),如果优先推理关系满足INJ,那么它可以用标准优先模型来表示。这个结论推广了Freund的结果。此外,我们证明,当语言是有限的时,我们的框架足以为任何注射式关系建立一个表示定理。