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A notion of an image structure associated with the canonical epistemic state is introduced. Based on it, we get a representation result for recovering contraction inference relations satisfying the condition weak conjunctive inclusion (wci) in terms of F-standard epistemic AGM states. In effect, this result establishes a representation theorem for belief contraction functions satisfying AGM postulates (k-1) – (k-7), and Rott's (wci) and (k-8c), and hence generalizes Rott's corresponding result in the finite framework.

The aim of this paper is to outline the background of constructing the medium logic and a survey of its development.

Although fruitful representation results induced by some kinds of injective models, e.g., filtered, ranked and quasi-linear injective models, etc., have been established in the literature, it is still an open problem to characterize the family of all injective inference relations in terms of rules. The type of postulates appearing in recent literature seems to be unable to characterize this family. This brings up an interesting theoretical problem: What kind of injective inference relations may be characterized by existent types of postulates? This paper makes an initial step to answer this question. To this end, a notion of a normal condition is introduced, which subsumes all Horn and non-Horn conditions presented in the literature. We obtain some results on injective models generating inferences characterized by normal conditions, and show that these injective models must be specific standard models. Moreover, for any set of injective models determined only by a structural property of preferential orders, if the family of inference relations induced by it can be characterized by normal conditions, then it must be a subset of filtered models in this circumstance. Thus, its associated inference relations satisfy the non-Horn rule disjunctive rationality.