A judgmental reconstruction of modal logic

@article{Pfenning2001AJR,
  title={A judgmental reconstruction of modal logic},
  author={Frank Pfenning and Rowan Davies},
  journal={Mathematical Structures in Computer Science},
  year={2001},
  volume={11},
  pages={511 - 540}
}
We reconsider the foundations of modal logic, following Martin-Löf's methodology of distinguishing judgments from propositions. We give constructive meaning explanations for necessity and possibility, which yields a simple and uniform system of natural deduction for intuitionistic modal logic that does not exhibit anomalies found in other proposals. We also give a new presentation of lax logic and find that the lax modality is already expressible using possibility and necessity. Through a… 
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