Humberstone, LloydMeyer, Robert2015-12-081367-0751http://hdl.handle.net/1885/32095The pure implicational and the multiplicative fragments of a range of propositional relevant (and other) logics are shown to have the property that any two formulas equivalent in such a logic are constructed from exactly the same propositional variables - as opposed to merely having (as the definition of relevance itself would require) some propositional variable in common.Keywords: Implicational logics; Relevance; Substructural logics200710.1093/jigpal/jzm0052015-12-08