Abstract

We introduce a basic intuitionistic conditional logic $\textsf{IntCK}$ that we show to be complete both relative to a special type of Kripke models and relative to a standard translation into first-order intuitionistic logic. We show that $\textsf{IntCK}$ stands in a very natural relation to other similar logics, like the basic classical conditional logic $\textsf{CK}$ and the basic intuitionistic modal logic $\textsf{IK}$. As for the basic intuitionistic conditional logic $\textsf{ICK}$ proposed in Weiss (_Journal of Philosophical Logic_, _48_, 447–469, 2019 ), $\textsf{IntCK}$ extends its language with a diamond-like conditional modality $\Diamond \hspace{-4.0pt}\rightarrow$, but its ( $\Diamond \hspace{-4.0pt}\rightarrow$ )-free fragment is also a proper extension of $\textsf{ICK}$. We briefly discuss the resulting gap between the two candidate systems of basic intuitionistic conditional logic and the possible pros and cons of both candidates.