We prove that there are continuum-many axiomatic extensions of the full Lambek calculus with exchange that have the deductive interpolation property. Further, we extend this result to both classical and intuitionistic linear logic as well as their multiplicative-additive fragments. None of the logics we exhibit have the Craig interpolation property, but we show that they all enjoy a guarded form of Craig interpolation.

翻译：我们证明了，在全兰贝克演算中具有交换性的连续统多个公理化扩张都具备演绎插值性质。进一步地，我们将这一结果推广到经典线性逻辑、直觉主义线性逻辑及其乘法-加法片段。我们所展示的此类逻辑均不满足克雷格插值性质，但我们证明它们都拥有一种有保护的克雷格插值形式。