Each Multiplicative Exponential Linear Logic (MELL) proof-net can be expanded into a differential net, which is its Taylor expansion. We prove that two different MELL proof-nets have two different Taylor expansions. As a corollary, we prove a completeness result for MELL: We show that the relational model is injective for MELL proof-nets, i.e. the equality between MELL proof-nets in the relational model is exactly axiomatized by cut-elimination.

@article{paperbot351,
  title = {Taylor expansion in linear logic is invertible},
  author = {Daniel de Carvalho},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 14, Issue 4},
  year = {2018},
  doi = {10.23638/lmcs-14(4:21)2018}
}