Obsessional experiments for linear logic proof-nets

We address the question of injectivity of coherent semantics of linear logic proof-nets. Starting from Girard's definition of experiment, we introduce the key-notion of ‘injective obsessional experiment’, which allows us to give a positive answer to our question for certain fragments of linear logic, and to build counter-examples to the injectivity of coherent semantics in the general case.

[1]  Jean-Yves Girard,et al.  Light Linear Logic , 1998, Inf. Comput..

[2]  Helmut Schwichtenberg,et al.  Normalisation by Evaluation , 1998, Prospects for Hardware Foundations.

[3]  Vincent Danos,et al.  Linear logic and elementary time , 2003, Inf. Comput..

[4]  Lorenzo Tortora de Falco,et al.  Denotational Semantics for Polarized (But-non-constrainted) LK by Means of the Additives , 1997, Kurt Gödel Colloquium.

[5]  Vincent Danos,et al.  A new deconstructive logic: linear logic , 1997, Journal of Symbolic Logic.

[6]  Jean-Yves Girard,et al.  A new constructive logic: classic logic , 1991, Mathematical Structures in Computer Science.

[7]  Jean-Yves Girard,et al.  On the Unity of Logic , 1993, Ann. Pure Appl. Log..

[8]  Olivier Danvy,et al.  Normalization by evaluation with typed abstract syntax , 2001, J. Funct. Program..

[9]  Eric Duquesne,et al.  Modèle cohérent des réseaux de preuve , 1994, Arch. Math. Log..

[10]  Olivier Laurent,et al.  Slicing Polarized Additive Normalization , 2022 .

[11]  Lorenzo Tortora de Falco,et al.  Polarisation des preuves classiques et renversement , 1996 .

[12]  Vincent Danos,et al.  Proof-nets and the Hilbert space , 1995 .

[13]  Lorenzo Tortora de Falco,et al.  Additives of linear logic and normalization - Part I: a (restricted) Church-Rosser property , 2003, Theor. Comput. Sci..

[14]  Jean-Yves Girard,et al.  Linear Logic , 1987, Theor. Comput. Sci..

[15]  Vincent Danos.  La Logique Linéaire appliquée à l'étude de divers processus de normalisation (principalement du Lambda-calcul) , 1990 .

[16]  Christian Retoré.  A Semantic Characterisation of the Correctness of a Proof Net , 1997, Math. Struct. Comput. Sci..