论文标题
所有逻辑II的POSET：Leibniz类和层次结构
The poset of all logics II: Leibniz classes and hierarchy
论文作者
论文摘要
Leibniz类是在术语等效逻辑，兼容扩展和一组逻辑集的非索引产品的形成下关闭的一类逻辑。我们研究所有莱布尼兹类的完整晶格，称为莱布尼兹层次结构。特别是，事实证明，在莱布尼兹层次结构中，真实性和断言逻辑的类别是聚会，而原始逻辑和等效逻辑的类别则可以符合。但是，最后两个类显示由仅由Meet-Prime逻辑组成的Leibniz条件确定。
A Leibniz class is a class of logics closed under the formation of term-equivalent logics, compatible expansions, and non-indexed products of sets of logics. We study the complete lattice of all Leibniz classes, called the Leibniz hierarchy. In particular, it is proved that the classes of truth-equational and assertional logics are meet-prime in the Leibniz hierarchy, while the classes of protoalgebraic and equivalential logics are meet-reducible. However, the last two classes are shown to be determined by Leibniz conditions consisting of meet-prime logics only.
