Published online by Cambridge University Press: 09 December 2019
| Valid | Invalid |
|---|---|
ϕ  χ, ϕ & χ ψ ⊨ ϕ ψ | ϕ □→ χ, χ ψ ⊨ ϕ ψ |
| ϕ χ, □[χ ⊃ ψ] ⊨ ϕ ψ | □[ϕ ⊃ χ], χ ψ ⊨ ϕ ψ |
ϕ ψ, ϕ  χ ⊨ ϕ & χ ψ | ϕ ψ ⊨ ϕ & χ ψ |
| □[ϕ ≡ χ], χ ψ ⊨ ϕ ψ | |
| ϕ χ, χ ϕ, χ ψ ⊨ ϕ ψ | |
| χ ϕ, χ & ϕ ψ ⊨ χ ψ | |
| χ ϕ, χ & ϕ ψ ⊨ χ ψ | |
| □[ϕ ⊃ ψ] ⊨ ϕ ψ |
(Further valid and invalid inference rules involving counterfactuals can be found in Lewis Reference Lewis1973b: 31–36 and Reference Lewis1973c.)
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