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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that In proof-theoretic semantics, a 'result' presupposes termination; Church–Rosser is silent on whether reduction terminates for arbitrary terms.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Infinite reduction sequences can carry semantic content through their limiting behavior, not requiring finite termination for meaning.
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    • 2.Church-Rosser's silence on termination reflects appropriate separation of concerns: confluence is independent of halting properties.
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    • 3.Proof-theoretic semantics need not assume all meaningful expressions terminate; divergence itself can be informationally significant.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Proof-theoretic semantics grounds meaning in constructive derivability, which intrinsically requires finite proof steps to establish content.
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    • 2.Church-Rosser guarantees unique normal forms when reduction terminates, but says nothing about whether all terms eventually reach one.
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    • 3.Non-terminating reductions produce no canonical result, making them semantically inert under constructivist interpretations of proof.
      ?

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