AI 中文总结
本文系统研究某些基本条件逻辑的波斯特完全扩张，确定了正则和正规的此类逻辑，证明相关嵌入定理类似结论，还表明某些基本条件逻辑有不可数多个扩张，其在条件规则下闭包放宽，对条件逻辑格结构及多模态逻辑有启示。
AI 中文摘要
如果一个逻辑是一致的但没有一致的真扩张，那么它就是波斯特完全的。在本文中，我们系统地研究了某些基本条件逻辑的波斯特完全扩张。我们确定了所有有限多个正则和正规的波斯特完全条件逻辑，并证明了马金森嵌入定理的类似结论。我们还表明，某些基本条件逻辑有不可数多个波斯特完全扩张，其中在条件特有的某些但不一定所有规则下的闭包被放宽。我们思考了我们的结果关于某些条件逻辑格的结构告诉了我们什么，也为多模态逻辑得出了一些启示。
英文摘要
A logic is Post complete if it is consistent but has no consistent proper extensions. In this article, we systematically investigate the Post complete extensions of certain basic conditional logics. We identify all of the finitely many regular and normal Post complete conditional logics, and prove analogues of Makinson's embedding theorems. We also show that certain basic conditional logics have uncountably many Post complete extensions for which closure under some, but not necessarily all, rules peculiar to the conditional are relaxed. We reflect on what our results tell us about the structure of certain lattices of conditional logics and also draw some morals for multimodal logic.
