This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. \({p\Rightarrow q}\) is thus defined as \({\lnot } \Diamond {(p \wedge \lnot q) \wedge } \Diamond {p \wedge } \Diamond {\lnot q}\). We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle’s theses and weak Boethius’ thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut.

本文研究了隐含条件句，这是一种连接词，旨在描述根据经验定义的一类自然语言条件句的逻辑行为，也称为隐含条件句，不包括让步和其他一些条件句。蕴涵条件句通过前件的可能性和后件的矛盾性加强了严格条件句。\({p\Rightarrow q}\)因此定义为\({\lnot } \Diamond {(p \wedge \lnot q) \wedge } \Diamond {p \wedge } \Diamond {\lnot q}\)。我们在自反正常克里普克语义中探索这个条件的逻辑属性，提供一个公理系统并证明它对于我们的语义来说是合理和完整的。隐含条件验证了及物性和对位性，我们认为它们是推理和交流的组成部分。但它只验证了强化先行词、右弱化、简化和理性单调性的有限版本。其中一些属性的明显反例被解释为由于上下文因素。最后，蕴涵条件句避免了实质蕴涵和严格蕴涵的悖论，验证了亚里士多德的命题和弱波爱提乌斯的命题等一些连接原则，以及条件句的一些根深蒂固的原则，如后件的合取、先件的析取、modus ponens，谨慎的单调性和削减。