Formulas for which Contraction is Admissible

A formula A is said to have the contractionproperty 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 contractionpropertyi it is a theorem. Adding the mix rule does not changethis 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.

• Type: Journal
• Year: 1998
• Where: IGPL
• Authors: Arnon Avron
• Keywords: Formula A, IGPL 1998, L B, Logic