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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 Order-invariant definability in FO(LFP) diverges from ordered FO(LFP) definability, making the logical capture of P order-sensitive.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Order-invariant and ordered FO(LFP) may capture identical problems; divergence in definability doesn't entail divergence in expressive power.
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    • 2.The practical relevance of order-invariance is unclear—real computation doesn't privilege order-independent definitions over order-dependent ones.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Order-invariant definability requires properties invariant across all orderings, a strictly stronger constraint than ordered definability.
      ?

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    • 2.P-completeness results depend on specific orderings; absent order-invariance, FO(LFP) captures only order-dependent fragments of P.
      ?

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    • 3.This divergence reveals that canonical logical characterizations of P require order structure, supporting order-sensitivity of computational complexity.
      ?

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