Coherence Under Commitment: Probing Generalization and Vacuous Memorization in LLM Logical Reasoning

• URL: http://arxiv.org/abs/2606.21083v1
• Date: Fri, 19 Jun 2026 04:12:56 GMT
• Title: Coherence Under Commitment: Probing Generalization and Vacuous Memorization in LLM Logical Reasoning
• Abstract summary: We introduce Coherence Under Commitment (CUC), a dual-query evaluation paradigm that jointly measures consistency and decisiveness.<n>CUC contributes three innovations: (1) a commitment score $c(varphi) = p(varphi) + p(lnotvarphi)$ quantifying probability mass allocated to decisive outcomes; (2) a textbfdeterministic elicitation protocol via normalized YES/NO log probabilities, eliminating sampling variance; and (3) a 3-way decision framework (True/False/Uncertain) operationalizing the coherence-commitment trade-off into metrics.
• Score: 0.9023847175654603
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language models (LLMs) deployed for logical reasoning in knowledge-intensive domains exhibit a subtle but critical failure: coherence can be vacuously achieved through systematic abstention. A model that withholds commitment to either entailment or refutation satisfies negation consistency while providing no utility. We introduce Coherence Under Commitment (CUC), a dual-query evaluation paradigm that jointly measures consistency and decisiveness. CUC contributes three innovations: (1) a commitment score $c(\varphi) = p(\varphi) + p(\lnot\varphi)$ quantifying probability mass allocated to decisive outcomes; (2) a \textbf{deterministic elicitation protocol} via normalized YES/NO log probabilities, eliminating sampling variance; and (3) a 3-way decision framework (True/False/Uncertain) operationalizing the coherence-commitment trade-off into metrics. Experiments on four open-weight LLMs (1B-3B) across 204 FOLIO examples expose a sharp frontier. Qwen2.5-3B achieves near-zero contradiction ($\mathbb{E}[v_{\mathrm{neg}}]{=}0.025$) but only $7.4\%$ coverage, while TinyLlama-1.1B reaches $79.4\%$ coverage with violations on every example. Coherence-only evaluation would rank the abstaining model first; CUC exposes this as vacuous, and the frontier generalizes to LogiQA~v2 ($ρ{=}0.97$). We argue that evaluation must report both coherence and non-vacuous commitment and release a toolkit for standardized assessment.

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