论文标题
关于矩阵的后果（扩展摘要）
On Matrix Consequence (Extended Abstract)
论文作者
论文摘要
这些结果是对矩阵结果模型理论的贡献。我们给出统一和统一后果关系的语义表征。至少以语义方式从未对这些特性进行单独处理。我们从纯粹的语义角度考虑了这些概念，并分别考虑了统一束/地图集的概念以及统一的逻辑矩阵类别的概念。然后，我们表明任何均匀的束都定义了统一的后果。如果结构后果是统一的，则其Lindenbaum地图集是均匀的。因此，任何结构后果都是均匀的，并且只有当它由均匀的束/地图集确定时。另一方面，任何均匀的矩阵都定义了均匀的结构后果。同样，均匀结构后果的Lindenbaum地图集是均匀的。因此，任何结构后果都是均匀的，并且只有当它由均匀束/地图集确定时。然后，我们将这些观察值应用于比较当一种语言是另一种语言的原始扩展时，用不同语言定义的结构后果关系。对于以一种（至少）（至少）一组句子变量的语言定义的任何结构性后果，如果这种后果是统一和均匀的，那么它和\ emph {wójcicki的后果}与之相对应，这是在给定语言的任何原始扩展中定义的。
These results are a contribution to the model theory of matrix consequence. We give a semantic characterization of uniform and couniform consequence relations. These properties have never been treated individually, at least in a semantic manner. We consider these notions from a purely semantic point of view and separately, introducing the notion of a uniform bundle/atlas and that of a couniform class of logical matrices. Then, we show that any uniform bundle defines a uniform consequence; and if a structural consequence is uniform, then its Lindenbaum atlas is uniform. Thus, any structural consequence is uniform if, and only if, it is determined by a uniform bundle/atlas. On the other hand, any couniform set of matrices defines a couniform structural consequence. Also, the Lindenbaum atlas of a couniform structural consequence is couniform. Thus, any structural consequence is couniform if, and only if, it is determined by a couniform bundle/atlas. We then apply these observations to compare structural consequence relations that are defined in different languages when one language is a primitive extension of another. We obtain that for any structural consequence defined in a language having (at least) a denumerable set of sentential variables, if this consequence is uniform and couniform, then it and the \emph{ Wójcicki's consequence} corresponding to it, which is defined in any primitive extension of the given language, are determined by one and the same atlas which is both uniform and couniform.
