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    The failure of polynomial boundedness has not been proven... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
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    42
    Home/Skepticism
    HistoryEditSee Inverse

    The failure of polynomial boundedness has not been proven for most familiar proof systems

    Skepticism
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.At present no superpolynomial lower bounds have been established for systems P1, P2, or P3
      ?

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    • 2.Proof complexity results separating proof systems are limited to specific systems such as resolution
      ?

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Absence of proof of superpolynomial lower bounds is not equivalent to absence of superpolynomial lower bounds in those systems.
      ?

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    • 2.Cook's conjecture (NP ≠ co-NP) implies no propositional proof system is polynomially bounded, which would contradict the implication of the claim.
      ?

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    • 3.The epistemological status of unproven mathematical conjectures with strong theoretical support differs from genuinely open empirical questions.
      ?

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    Reason against 2 of 2
    ?
    • 1.Krajíček and Pudlák established conditional superpolynomial lower bounds for Frege systems relative to plausible cryptographic assumptions.
      ?

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    • 2.Conditional results grounded in well-evidenced complexity assumptions constitute substantial evidence against polynomial boundedness even absent unconditional proofs.
      ?

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    • 3.A claim about 'failure not being proven' misleads by ignoring the established hierarchy of indirect proof-theoretic evidence in the field.
      ?

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    Related

    A claim about 'failure not being proven' misleads by ignoring the established hi...Absence of proof of superpolynomial lower bounds is not equivalent to absence of...At present no superpolynomial lower bounds have been established for systems P1,...Conditional results grounded in well-evidenced complexity assumptions constitute...
    +4 moreShow less
    Cook's conjecture (NP ≠ co-NP) implies no propositional proof system is polynomi...Krajíček and Pudlák established conditional superpolynomial lower bounds for Fre...Proof complexity results separating proof systems are limited to specific system...The epistemological status of unproven mathematical conjectures with strong theo...

    Similar

    No proof system has yet been shown to be polynomially bounded87%Resolution is not polynomially bounded as a proof system86%A proof system is polynomially bounded only if all tautologies have pr...84%Polynomial proof systems (polynomially bounded proof systems) likely d...83%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    as the set of formulas derivable from some set of axioms of \(\Gamma_{\mathcal{L}}\) rather than the class of formulas true in all structures – the validity problem is understood to coincide with the problem of deciding whether \(\phi\) is derivable from \(\Gamma_{\mathcal{L}}\). In such cases, the satisfiability and model checking problems are generally not considered. The problems \(\sc{SATISFIABILITY}_{\mathcal{L}}\), \(\sc{VALIDITY}_{\mathcal{L}}\), and \(\sc{MODEL}\ \sc{CHECKING}_{\mathcal{
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit