Coherent Interaction Graphs

04/15/2019

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by   Lê Thành Dũng Nguyên, et al.

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We introduce the notion of coherent graphs, and show how those can be used to define dynamic semantics for Multiplicative Linear Logic (MLL) extended with non-determinism. Thanks to the use of a coherence relation rather than mere formal sums of non-deterministic possibilities, our model enjoys some finiteness and sparsity properties. We also show how studying the semantic types generated by a single "test" within our model of MLL naturally gives rise to a notion of proof net, which turns out to be exactly Retoré's R&B-cographs. This revisits the old idea that multplicative proof net correctness is interactive, with a twist: types are characterized not by a set of counter-proofs but by a single non-deterministic counter-proof.