The relational model is injective for multiplicative exponential linear logic (without weakenings)

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• 作者：Daniel de Carvalho^a ; ^{carvalho@lipn.univ-paris13.fr} ; Lorenzo Tortora de Falco^b ; ^{tortora@uniroma3.it}
• 关键词：03F05 ; 03F07 ; 03F52
• 刊名：Annals of Pure and Applied Logic
• 出版年：2012
• 期刊代码：4_01680072
• 类别：cp
• 出版时间：September, 2012
• 卷：163
• 期：9
• 页码：1210-1236
• 文件大小：513 K

摘要

We show that for Multiplicative Exponential Linear Logic (without weakenings) the syntactical equivalence relation on proofs induced by cut-elimination coincides with the semantic equivalence relation on proofs induced by the multiset based relational model: one says that the interpretation in the model (or the semantics) is injective. We actually prove a stronger result: two cut-free proofs of the full multiplicative and exponential fragment of linear logic whose interpretations coincide in the multiset based relational model are the same 鈥渦p to the connections between the doors of exponential boxes鈥?