$𝒩𝒦p$

$𝒩𝒦p$ is a natural deduction proof system for classical propositional logic. It is identical to NJp except that it replaces the rule ${\perp }_i$ with the rule:

$$\frac{\mathrm{\Gamma },\mathrm{\neg }\alpha \Rightarrow \perp }{\mathrm{\Gamma }\Rightarrow \alpha }({\perp }_c),\text{ where }\alpha \text{ is atomic}.$$