An Intuitionistically Complete System of Basic Intuitionistic Conditional Logic

Abstract We introduce a basic intuitionistic conditional logic IntCK 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 IntCK stands in a very natural relation to other similar logics, like the basic classical conditional logic CK CK and the basic intuitionistic modal logic IK IK. As for the basic intuitionistic conditional logic ICK ICK proposed in Weiss (Journal of Philosophical Logic, 48, 447–469, 2019), IntCK IntCK extends its language with a diamond-like conditional modality -4. 0pt ◊ →, but its (-4. 0pt ◊ →) -free fragment is also a proper extension of ICK 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.