Various surveys I've looked at relevance logic mention Ackermanns admissibility of gamma rule. I've not come across the term in logic before, what is it, how is it used and is it also important outside of relvance logic?
Ackermann's Rule Gamma is the rule that from "├── A->B" and "├── A", one may infer "├── B," where "->" denotes the material conditional. (Equivalently, from "├── ~A V B" and "├── A", infer "├── B.")
Note that this is distinct from modus ponens or disjunctive syllogism; this is the rule that if ~A V B is a theorem and A is a theorem then B, too, is a theorem. Such a distinction is clear in, e.g., Rule Necessitation in modal logics; from "├── A," infer "├── L A," where "L" denotes necessity. This clearly doesn't mean that a theory is closed under necessitation, merely that all theorems are necessary.