Proof nets for unit-free multiplicative-additive linear logic

  • Authors:

  • Dominic J. D. Hughes;Rob J. Van Glabbeek

  • Affiliations:

  • Stanford University, Stanford, CA;Stanford University, Stanford, CA

  • Venue:
  • ACM Transactions on Computational Logic (TOCL)
  • Year:
  • 2005

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Abstract

A cornerstone of the theory of proof nets for unit-free multiplicative linear logic (MLL) is the abstract representation of cut-free proofs modulo inessential rule commutation. The only known extension to additives, based on monomial weights, fails to preserve this key feature: a host of cut-free monomial proof nets can correspond to the same cut-free proof. Thus, the problem of finding a satisfactory notion of proof net for unit-free multiplicative-additive linear logic (MALL) has remained open since the inception of linear logic in 1986. We present a new definition of MALL proof net which remains faithful to the cornerstone of the MLL theory.