I have a paper about the open problem of G. Metcalfe and F. Montagna (see. Substructural fuzzy logics. Journal of Symbolic Logic, 7(3):834–864, 2007). This paper had been rejected by Journal of Symbolic Logic and Fuzzy sets and systems. The main reason is as follows.
Generally, a hypersequents is defined as a multi-set of sequents, but I define it as a set of sequents, and thus the external contraction rule (EC) is redundant, which greatly simplifies the proof of density elimination for all hypersequent systems. The referee (Maybe the referee of JSL just is the one of FSS) think that such a definition is wrong. I think that my paper have no errors after careful inspection. The reason that such a definition is feasible was clarified in my paper.
Can you read my paper and judge whether it is a wrong proof? I also attach my answers to the referee’s comments. Thank you very much.