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Dissymetrical Linear Logic


This paper is devoted to design computational systems of linear logic (i.e. systems in which, notably, the non linear and structural phenomena which arise during the cut-elimination process are taken in charge by specific modalities, the exponentials: ! and ?). The systems designed are "intermediate" between Intuitionistic LL and Classical LL. Methodologically, the focus is put on how to break the symmetrical interdependency between ! and ? which prevails in Classical LL-and this without to loose the computational properties (closure by cut-elimination, atomizability of axioms). Three main systems are designed (Dissymetrical LL, semi-functorial Dissymetrical LL, semi-specialized Dissymetrical LL), where, in each of them, ! and ? play well differentiated roles.
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hal-03815339 , version 1 (14-10-2022)


  • HAL Id : hal-03815339 , version 1


Jean-Baptiste Joinet. Dissymetrical Linear Logic. TLLA-Linearity (FLoC 2022), Jul 2022, Haifa, Israel. ⟨hal-03815339⟩
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