Admissible rule

Given a formal system $(L, I)$ , an inference rule $𝑅$ is said to be admissible iff $I' = I \cup {𝑅}$ gives the same Syntactic formal theory as $I$ , logic i.e.

T h (L, I) = T h (L, I') .

Informally, the inclusion of $𝑅$ does not affect the strength of the formal system. Another (at least constructively) equivalent definition is that there exists an algorithm for turning derivations in $T h (L, I')$ into derivations in $T h (L, I) .$

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Admissible rule

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