  This is not the only way to restrict premise combination. Girard (1987) introduced linear logic as a model for processes and resource use. The idea in this account of deduction is that resources must be used (so premise combination satisfies the relevance criterion) and they do not extend indefinitely. Premises cannot be \(re\)-used. So, I might have \(X,X \vdash A\), which says that I can use \(X\) twice to get \(A\). I might not have \(X \vdash A\), which says that I can use \(X\) once alone to get \(A\). A helpful introduction to linear logic is given in Troelstra’s Lectures on Linear Logic (1992). There are other formal logics in which the contraction rule (from \(X,X \vdash A\) to \(X \vdash A)\) is absent. Most famous among these are Łukasiewicz’s many-valued logics. There has been a sustained interest in logics without this rule because of Curry’s paradox (Curry 1977, Geach 1995; see also Restall 1994 in Other Internet Resources). 