Abstract
We define proof nets for cyclic multiplicative linear logic as edge bi-coloured graphs. Our characterization is purely graph theoretical and 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).
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Abrusci, V.M., Maringelli, E. A New Correctness Criterion for Cyclic Proof Nets. Journal of Logic, Language and Information 7, 449–459 (1998). https://doi.org/10.1023/A:1008354130493
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DOI: https://doi.org/10.1023/A:1008354130493