In this paper, we axiomatize the deontic logic in Fusco (2015), which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the restrictions Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to “lift” a Kripke frame for a one-dimensional modal logic into two dimensions.

在本文中，我们公理化了 Fusco (2015) 中的道义逻辑，该逻辑使用受 Stalnaker 启发的对角接受说明和析取的二维说明来处理罗斯悖论和自由选择许可之谜。因此，涉及析取的有效性是先验的，而不是必要的。我们展示了如何公理化二维析取，以便布尔析取的引入/消除规则可以被视为更一般的二维规则的一维投影。这些完整性结果有助于明确 Fusco 的帐户必须对自由选择推理施加的限制。它们也具有独立的兴趣，因为它们提出了有关如何将一维模态逻辑的 Kripke 框架“提升”为二维的难题。