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P (φ ∨ ψ) ⊨ P φ ∧ P ψ.

By drawing on the resources of exact truthmaker semantics, we avoid the standard problems associated with (FCP).

Our logic is a positive propositional deontic logic, i.e. it neither has negation nor any kind of implication. The connectives are simply ∨, ∧ and the permission operator P. Notably, the system has no theorems. We give a sound and complete axiomatization in terms of deducibility statements φ ⊢ ψ.

We then study extensions of the system with certain plausible principles for permission. In particular, we’ll determine semantic conditions that are equivalent to the validity of Pφ ∧ Pψ ⊨ P(φ ∨ ψ) and of P (φ ∧ ψ) ⊨ P φ ∧ P ψ.

(This is a joint work with Albert Anglberger.)