 Yet another logical system that is closely related to relevance logic is William Parry’s logic of Analytic Implication. Analytic Implication is motivated by the desire to satisfy a very strong form of variable-sharing. No implication \(A\rightarrow B\) is provable in this logic unless \(\mathbf{all}\) the variables in \(B\) are contained in \(A\). In order to satisfy this strong variable-sharing principle, the principle of disjunction introduction needs to be restricted. So, instead of having \(A\rightarrow(A\vee B)\) as a theorem for all formulas \(A\) and \(B\), this schema is valid only when all the propositional variables in \(B\) are also in \(A\). The principle of contraposition and some transitivity principles for implication also have to be restricted. 