In this article, I provide Urquhart-style semilattice semantics for three connexive logics in an implication-negation language (I call these “pure theories of connexive implication”). The systems semantically characterized include the implication-negation fragment of a connexive logic of Wansing, a relevant connexive logic recently developed proof-theoretically by Francez, and an intermediate system that is novel to this article. Simple proofs of soundness and completeness are given and the semantics is used to establish various facts about the systems (e.g., that two of the systems have the variable sharing property). I emphasize the intuitive content of the semantics and discuss how natural informational considerations underly each of the examined systems.

在本文中，我为蕴含否定语言中的三个连接逻辑提供了厄克特式的半格语义（我称这些为“连接蕴涵的纯理论”）。语义表征的系统包括Wansing的连接逻辑的蕴涵否定片段，Francez最近在理论上证明的相关连接逻辑，以及本文新颖的中间系统。给出了健全性和完整性的简单证明，并使用语义来建立有关系统的各种事实（例如，两个系统具有变量共享属性）。我强调语义的直观内容，并讨论自然信息考虑如何成为每个检查系统的基础。