Filling in the semantics for intuitionistic conditional logic
This work addresses a foundational gap in logic theory for researchers in mathematical logic and formal semantics, though it appears incremental as it builds on existing canonical model constructions.
The paper tackled the problem of proving completeness for intuitionistic conditional logics by developing a fill-in method to transfer results from descriptive conditional frames to more general conditional frames, achieving completeness across a wide variety of such logics.
We prove completeness results for a wide variety of intuitionistic conditional logics. We do so by first using a canonical model construction obtain completeness with respect to descriptive conditional frames, and then introducing the fill-in method to transfer this to classes of conditional frames without extra structure. The fill-in method closes the gap between descriptive conditional frames, which do not have a canonical underlying frame, and conditional frames.