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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