We study the relations between Multiplicative Exponential Linear Logic (mELL) and Baillot-Mazza Linear Logic by Levels (mL 3). We design a decoration-based translation between propositional mELL and propositional mL 3. The translation preserves the cut elimination. Moreover, we show that there is a proof net of second order mELL that cannot have a representative ∏ ′ in second order mL 3 under any decoration. This suggests that levels can be an analytical tool in understanding the complexity of second order quantifier. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Gaboardi, M., Roversi, L., & Vercelli, L. (2009). A by-level analysis of multiplicative exponential linear logic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5734 LNCS, pp. 344–355). https://doi.org/10.1007/978-3-642-03816-7_30
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