The main result proves Lyndon’s and Craig’s interpolation properties for the logic of strict implication |${\textsf{F}}$|⁠, with a purely syntactical method. A cut-free G3-style sequent calculus |$ {\textsf{GF}} $| and its single-succedent variant |$ \textsf{GF}_{\textsf{s}} $| are introduced. |$ {\textsf{GF}} $| can be extended to a G3-variant of the sequent calculus GBPC3 for Visser’s basic logic. Also a simple syntactic proof of known embedding result of |$ {\textsf{F}} $| into |$ {\textsf{K}} $| is provided. An extension of |$ {\textsf{F}} $|⁠, namely |$ \textsf{FD}, $| is considered as well.

中文翻译：

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Lyndon的插值属性用于严格蕴涵的逻辑

主要结果证明了Lyndon和Craig的插值属性具有严格的逻辑意义| $ {\ textsf {F}} $ |⁠，这是一种纯粹的语法方法。无割G3风格后续演算| $ {\ textsf {GF}} $ | 及其单后继变量| $ \ textsf {GF} _ {\ textsf {s}} $ | 介绍。| $ {\ textsf {GF}} $ | 对于Visser的基本逻辑，可以将其扩展为后续演算GBPC3的G3变量。也是| $ {\ textsf {F}} $ |的已知嵌入结果的简单句法证明。变成| $ {\ textsf {K}} $ | 提供。的扩展$ {\ textsf {F}} $ | |⁠，即| $ \ textsf {FD}，$ | 也被认为是。