The inclusion of axioms that eliminate modal distinctions within a deductive system. In the case of relevant logics or logics of strict implication, the necessity of a formula $\phi$ is expressible as $\left(\phi \to \phi \right)\to \phi$. Hence, demodalizing a deductive system involves imposing the equivalence of $\phi$ and $\left(\phi \to \phi \right)\to \phi$ for all formulae $\phi$. For example, the addition of the demodalizer axiom scheme:

to the relevant system $\text{E}$ or the logic of strict implication $\text{S}4$ yields the demodalized $\text{R}$ and the classical propositional calculus, respectively.