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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that The failure of polynomial boundedness has not been proven for most familiar proof systems

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 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 for 2 of 2
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    • 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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