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    Clarke's vector-algebraic framework therefore cannot yiel... — Carmelics
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    Challenges→Degrees of entailment can be construed in terms of entailment probabilities between logical forms of premise and hypothesis sentences.

    Clarke's vector-algebraic framework therefore cannot yield genuine entailment probabilities, only heuristic similarity scores mislabeled as such.

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    Reasons For

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    • 1.Vector similarity measures cosine distance, which reflects semantic proximity, not logical entailment relations required for valid inference.
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    • 2.Clarke's framework lacks formal proof that vector operations preserve logical consequence, only that they correlate with human similarity judgments.
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    • 3.Genuine entailment requires necessity: P entails Q means Q is true in all models where P is true. Vector scores provide only statistical associations.
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    Reasons Against

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    • 1.The distinction between 'heuristic similarity' and 'entailment probability' may be terminological rather than substantive if both track valid inference.
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    • 2.Probabilistic entailment (not classical entailment) is the appropriate standard for natural language, where vector methods can formalize conditional likelihood.
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    • 3.Clarke's framework can be formally validated empirically: if vector probabilities systematically predict human inference judgments, the mislabeling charge fails.
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    Related

    Clarke's framework can be formally validated empirically: if vector probabilitie...Clarke's framework lacks formal proof that vector operations preserve logical co...Degrees of entailment can be construed in terms of entailment probabilities betw...Genuine entailment requires necessity: P entails Q means Q is true in all models...
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    Probabilistic entailment (not classical entailment) is the appropriate standard ...The distinction between 'heuristic similarity' and 'entailment probability' may ...Vector similarity measures cosine distance, which reflects semantic proximity, n...

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