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    Cut elimination is a metatheorem that must be proved for ... — Carmelics
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    Challenges→In Gentzen systems, if a connective does not appear in the conclusion of a proof, it will not appear in the proof at all.

    Cut elimination is a metatheorem that must be proved for each Gentzen system, not a universal structural feature of all such systems.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Different Gentzen systems (LK, LJ, modal logics) have distinct structural rules, so cut-elimination proofs vary significantly across them.
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    • 2.Cut elimination fails for some well-motivated Gentzen systems (e.g., relevant logics, paraconsistent systems), showing it's not universally guaranteed.
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    • 3.The cut-elimination proof depends on induction on formula complexity, which requires system-specific design of inference rules to ensure success.
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    Reasons Against

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    Reason against
    ?
    • 1.Cut elimination holds for all standard Gentzen sequent calculi precisely because the formalism is designed with this structural property in mind.
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    • 2.When cut elimination fails in some system, the failure indicates the system is non-standard or poorly designed, not that cut elimination is non-universal.
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    • 3.The proof strategy for cut elimination (proving by induction on cut rank) is fundamentally uniform across Gentzen systems, not fundamentally system-specific.
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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Cut elimination fails for some well-motivated Gentzen systems (e.g., relevant lo...Cut elimination holds for all standard Gentzen sequent calculi precisely because...Different Gentzen systems (LK, LJ, modal logics) have distinct structural rules,...In Gentzen systems, if a connective does not appear in the conclusion of a proof...
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    The cut-elimination proof depends on induction on formula complexity, which requ...The proof strategy for cut elimination (proving by induction on cut rank) is fun...When cut elimination fails in some system, the failure indicates the system is n...

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    Perspectives
    2 (1 for, 1 against)
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    1 edit