Conjectured equality Lmin = Log(Cuc) = Log(Cquc)

Establish that the minimal normal intuitionistic modal logic Lmin coincides with both Log(Cuc), the logic of upward confluent frames, and Log(Cquc), the logic of quasi-upward confluent frames.

Background

The authors introduce Lmin as a candidate for the minimal normal intuitionistic modal logic under their new semantics. They conjecture that this logic matches the validities over upward confluent and quasi-upward confluent frames, suggesting a tight correspondence potentially provable via unravelling transformations.