单可表示类的特征

择优模型是目前常识推理领域中最常用的语义结构之一。在择优模型中有一类重要的模型－单射择优模型，近年来，众多的学者对该模型类从各种角度进行了研究，但一个重要而基本的问题，即何种类型的择优后承具有单射择优模型，虽经多位学者的研究到现在仍然悬而未解。目前，最好的结果Freund在有限语言限制下证明了“择优后承具有单射择优模型当且仅当它满足弱析取合理性”。文中提出择优模型的一种转换，将此转换应用于Kraus,Leham及Magidor提出的KLM模型上，在一般语言框架下证明了“满足弱析取合理性的择优后承必具有单射择优模型”，从而将该问题的研究推进了一步。

On Characteristics of Injective Representability Inference Relation

Preferential model is one kind of well known semantic structures in commonsence reasoning. Among them, injective preferential models are important and interesting, and some researchers have pay attention to exploring them from various angles. Michael Freund showed that,when the language is finite,a preferential inference relation may be generated by an injective preferential model if and only if it satisfies Weak Disjunctive Rationality (WDR, for short). However, when the language is infinite, how to characterize all preferential relations that may be generated by an injective preferential model is open. Recently, R.Pino Perez and Carlos Uzcategui showed that, if the preferential relation satisfies the property WDR then it can be represented by an essential pre structure. Unfortunately they do not prove that this structure is transitive in this case, and so far it is unknown whether this structure is a preferential model. However this result suggests that the property WDR could be considered as a postulate that characterizes injective relations even when the language is infinite. This paper presents a method to transform the model introduced by S.Kraus, D.Lehman and M.Magidor to a structure which is homologous with injective preferential model. Let |~ be a preferential relation and W be the KLM model associated with it, we show that, if the relation |~ satisfies the property WDR then this structure is an injective preferential model and represents the relation |~. Consequently, we partly solve the above problem and get the following result: in any language, if a preferential inference relation satisfies the property WDR then it can be generated by an injective preferential model.