n this paper, we propose a bundle-based framework of deontic logic with permission, obligation, and prohibition, based on our previous work on free choice (strong) permission. The key is to introduce the negated action types such that $\neg\alpha$ captures the idea of \textit{not doing $\alpha$}. This negation can naturally connect weak obligation and prohibition to strong permission. It also helps to define weak permission and strong obligation. Under various model classes, we give several sound and complete proof systems with strong permission, weak obligation, and prohibition modalities. We also compare our work with Fine’s deontic logic based on truthmaking semantics.

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