On the Jordan-Hölder decomposition of proof nets

Q. Puite, H. Schellinx

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    Abstract

    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 there exists a Jordan-Hölder decomposition of H0(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 H0(G) and the possible ‘construction-orders’ of the par-net underlying G.
    Original languageEnglish
    Pages (from-to)59-65
    Number of pages7
    JournalArchive for Mathematical Logic
    Volume37
    Issue number1
    DOIs
    Publication statusPublished - 1997

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