We provide a logical matrix semantics and a Gentzen-style sequent calculus for the first-degree entailments valid in W. T. Parry’s logic of Analytic Implication. We achieve the former by introducing a logical matrix closely related to that inducing paracomplete weak Kleene logic, and the latter by presenting a calculus where the initial sequents and the left and right rules for negation are subject to linguistic constraints.

中文翻译：

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帕里解析蕴涵逻辑的简单逻辑矩阵和后续演算

我们为WT Parry的分析蕴涵逻辑中有效的一级条件提供了逻辑矩阵语义和Gentzen式顺序演算。我们通过引入与诱导超完备弱Kleene逻辑密切相关的逻辑矩阵来实现前者，而通过提出一种将初始序列和否定左，右规则都受到语言约束的演算来实现后者。