An Intuitionistically Complete System of Basic Intuitionistic Conditional Logic.

We introduce a basic intuitionistic conditional logic 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 IntCK stands in a very natural relation to other similar logics, like the basic classical conditional logic CK and the basic intuitionistic modal logic IK . As for the basic intuitionistic conditional logic ICK proposed in Weiss (Journal of Philosophical Logic, 48, 447–469, 2019), IntCK extends its language with a diamond-like conditional modality ◊ → , but its ( ◊ → )-free fragment is also a proper extension of 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. [ABSTRACT FROM AUTHOR]