## Section: New Results

### On the Decision Problem for MELL

Participant : Lutz Straßburger.

The decision problem for multiplicative exponential linear logic (MELL) is one of the most important open problems in the are of linear logic. in 2015 there has been an attempt by Bimbò to prove the decidability of MELL. However, we have found several mistakes in that work, and the main mistake is so serious that there is no obvious fix, and therefore the decidability of MELL remains to be open. As a side effect, our work contains a complete (syntactic) proof of the decidability of the relevant version of MELL, that is the logic obtained from MELL by replacing the linear logic contraction rule by a general unrestricted version of the contraction rule. These results are presented in [27].