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    In proof-theoretic semantics, a 'result' presupposes term... — Carmelics
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    Supports→The claim that the Church–Rosser theorem guarantees a unique final result is a slight overstatement

    In proof-theoretic semantics, a 'result' presupposes termination; Church–Rosser is silent on whether reduction terminates for arbitrary terms.

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    Reasons For

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    Reason for
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    • 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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    Reasons Against

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    Reason against
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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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    Related

    Church-Rosser guarantees unique normal forms when reduction terminates, but says...Church-Rosser's silence on termination reflects appropriate separation of concer...Infinite reduction sequences can carry semantic content through their limiting b...Non-terminating reductions produce no canonical result, making them semantically...
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    Proof-theoretic semantics grounds meaning in constructive derivability, which in...Proof-theoretic semantics need not assume all meaningful expressions terminate; ...The claim that the Church–Rosser theorem guarantees a unique final result is a s...

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