A New Correctness Criterion for Cyclic Proof Nets

  • Authors:
  • V. Michele Abrusci;Elena Maringelli

  • Affiliations:
  • Logica, Dipartimento di Filosofia, Università di Roma Tre, via Magenta 5, 00185 Rome, Italy (E-mail: Email: abrusci@uniroma3.it);Logica, Dipartimento di Filosofia, Università di Roma Tre, via Magenta 5, 00185 Rome, Italy (E-mail: Email: abrusci@uniroma3.it)

  • Venue:
  • Journal of Logic, Language and Information
  • Year:
  • 1998

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Abstract

We define proof nets for cyclic multiplicative linear logic as edge bi-coloured graphs.Our characterization is purely graph theoreticaland works without further complication for proof nets with cuts, which are usually harder to handle in the non-commutative case. This also provides a new characterization of the proof nets for the Lambek calculus (with the empty sequence) which simply are a restriction on the formulas to be considered(which are asked to be intuitionistic).