Abstract
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 \({\it \Pi}\) of second order mELL that cannot have a representative \({\it \Pi'}\) 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.
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Gaboardi, M., Roversi, L., Vercelli, L. (2009). A By-Level Analysis of Multiplicative Exponential Linear Logic. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_30
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DOI: https://doi.org/10.1007/978-3-642-03816-7_30
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