An Intuitionistically Complete System of Basic Intuitionistic Conditional Logic
Grigory K. Olkhovikov · Journal of Philosophical Logic · 2024
Abstract We introduce a basic intuitionistic conditional logic $$\textsf{IntCK}$$ 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 $$\textsf{IntCK}$$ IntCK stands in a very natural relation to other similar logics, like the basic classical conditional logic $$\textsf{CK}$$ CK and the basic intuitionistic modal logic $$\textsf{IK}$$ IK . As for the basic intuitionistic conditional logic $$\textsf{ICK}$$ ICK proposed in Weiss (Journal of Philosophical Logic, 48, 447–469, 2019), $$\textsf{IntCK}$$ 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 $$\textsf{ICK}$$ 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.