Computer Science Logic

Volume 2471 of the series Lecture Notes in Computer Science pp 151-166


Proofnets and Context Semantics for the Additives

  • Harry G. MairsonAffiliated withComputer Science Department, Brandeis University Waltham
  • , Xavier RivalAffiliated withÉcole Normale Superieure

* Final gross prices may vary according to local VAT.

Get Access


We provide a context semantics for Multiplicative-Additive Linear Logic (MALL), together with proofnets whose reduction preserves semantics, where proofnet reduction is equated with cut-elimination on MALL sequents. The results extend the program of Gonthier, Abadi, and Lévy, who provided a “geometry of optimal λ-reduction” (context semantics) for λ-calculus and Multiplicative-Exponential Linear Logic (MELL). We integrate three features: a semantics that uses buses to implement slicing; a proofnet technology that allows multidimensional boxes and generalized garbage, preserving the linearity of additive reduction; and finally, a read-back procedure that computes a cut-free proof from the semantics, a constructive companion to full abstraction theorems.