Formulas for which Contraction is Admissible

Abstract
A formula A is said to have the contraction property in a logic L i whenever A;A;? `L B (when ? is a multiset) also A;? `L B. In MLL and in MALL without the additive constants a formula has the contractionproperty i it is a theorem. Adding the mix rule does not change this fact. In MALL (with or without mix) and in a ne logic A has the contraction property i either A is provable or A is equivalent to the additive constant 0. We present some general proof-theoretical principles from which all these results (and others) easily follow
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