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    The subformula property—on which the claim depends—fails ... — 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.

    The subformula property—on which the claim depends—fails for systems with non-standard structural rules such as those modeling modal or relevant logics.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Modal and relevant logics require structural rules (like weakening restrictions) that allow formulas outside the main proof to affect validity.
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    • 2.Subformula property holds only when all premises and conclusions appear in derivation steps—non-standard rules violate this requirement.
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    • 3.Loss of subformula property in these systems necessitates different proof-theoretic tools, confirming the claim's underlying logical distinction.
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    Reasons Against

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    Reason against
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    • 1.Many modal and relevant logic systems retain restricted subformula properties through careful rule design, limiting the claim's scope.
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    • 2.The claim conflates structural rule modification with complete subformula failure—some non-standard systems preserve partial subformularity.
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    • 3.Successful proof systems exist for modal/relevant logics using analytic tableaux or sequent variants that maintain meaningful subformula constraints.
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    Connections

    2 topics

    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    In Gentzen systems, if a connective does not appear in the conclusion of a proof...Loss of subformula property in these systems necessitates different proof-theore...Many modal and relevant logic systems retain restricted subformula properties th...Modal and relevant logics require structural rules (like weakening restrictions)...
    +3 moreShow less
    Subformula property holds only when all premises and conclusions appear in deriv...Successful proof systems exist for modal/relevant logics using analytic tableaux...The claim conflates structural rule modification with complete subformula failur...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit