Abstract

) Olivier Laurent Institut de Math'ematiques de Luminy CNRS-Marseille, France olaurent@iml.univ-mrs.fr Abstract. We define a notion of polarization in linear logic (LL) coming from the polarities of Jean-Yves Girard's classical sequent calculus LC [4]. This allows us to define a translation between the two systems. Then we study the application of this polarization constraint to proofnets for full linear logic described in [7]. This yields an important simplification of the correctness criterion for polarized proof-nets. In this way we obtain a system of proof-nets for LC. The study of cut-elimination takes an important place in proof-theory. Much work is spent to deal with commutation of rules for cut-elimination in sequent calculi. The introduction of proof-nets (see [7] for instance) solves commutation problems and allows us to define a clear notion of reduction and complexity. In [4], Jean-Yves Girard defines the sequent calculus LC using polarities. LC is a refinement...

Citations

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