1. Roberto Maieli & Quintijn Puite (2005). Modularity of Proof-Nets. Archive for Mathematical Logic 44 (2):167-193.
    When we cut a multiplicative proof-net of linear logic in two parts we get two modules with a certain border. We call pretype of a module the set of partitions over its border induced by Danos-Regnier switchings. The type of a module is then defined as the double orthogonal of its pretype. This is an optimal notion describing the behaviour of a module: two modules behave in the same way precisely if they have the same type.In this paper we define (...)
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  2. Richard Moot & Quintijn Puite (2002). Proof Nets for the Multimodal Lambek Calculus. Studia Logica 71 (3):415-442.
    We present a novel way of using proof nets for the multimodal Lambek calculus, which provides a general treatment of both the unary and binary connectives. We also introduce a correctness criterion which is valid for a large class of structural rules and prove basic soundness, completeness and cut elimination results. Finally, we will present a correctness criterion for the original Lambek calculus Las an instance of our general correctness criterion.
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  3. Quintijn Puite & Harold Schellinx (1997). On the Jordan-Hölder Decomposition of Proof Nets. Archive for Mathematical Logic 37 (1):59-65.
    Having defined a notion of homology for paired graphs, Métayer ([Ma]) proves a homological correctness criterion for proof nets, and states that for any proof net $G$ there exists a Jordan-Hölder decomposition of ${\mathsf H}_0(G)$ . This decomposition is determined by a certain enumeration of the pairs in $G$ . We correct his proof of this fact and show that there exists a 1-1 correspondence between these Jordan-Hölder decompositions of ${\mathsf H}_0(G)$ and the possible ‘construction-orders’ of the par-net underlying $G$.
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