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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that Resolution is not polynomially bounded.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Haken's 1985 proof relies on a specific syntactic formalization of PHP_n; alternative encodings may yield structurally distinct tautologies with shorter proofs.
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    • 2.The polynomial boundedness criterion is encoding-relative, so no single tautology family establishes system-wide unprovability across all representations.
      ?

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    Reason for 2 of 2
    ?
    • 1.Cook and Reckhow's framework presupposes a classical notion of proof size; non-classical proof-theoretic accounts (e.g., deep inference) dissolve the exponential lower bound.
      ?

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    • 2.Resolution's complexity profile is a property of the formalism, not of the underlying logical truths, so the claim conflates proof-system limitations with logical necessity.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Any resolution proof of PHP_n must have size at least exponential in n (Haken's result).
      ?

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    • 2.A proof system is polynomially bounded only if all tautologies have proofs of size polynomial in the size of the tautology.
      ?

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