An algebraic semantics, based on factor algebras, for one-way and two-way implicative verbs is proposed. Implicative verbs denote elements of filters or of ideals generated by identity functions in factor algebras. This semantics explains in particular the problem of implicational equivalence raised by two-way implicative verbs, and shows that the negation necessary to establish the implicativity of these verbs is the negation which preserves the presuppositions of sentences with implicative verbs. In addition, it follows from the proposed semantics that any two implicative verbs denoting in the same algebra but belonging to different categories, are semantically related.

中文翻译：

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走向蕴涵的代数语义

提出了一种基于因子代数的单向和双向隐含动词的代数语义。隐含动词表示过滤器的元素或由因子代数中的恒等函数生成的理想元素。这种语义学特别解释了双向隐含动词引发的隐含对等问题，表明确立这些动词的隐含性所必需的否定是保留含含动词的句子的预设的否定。此外，根据提议的语义，任何两个表示在同一代数中但属于不同类别的隐含动词在语义上是相关的。