aiqbench analysis
This paper introduces SIV, a new evaluation metric for natural language-to-first-order logic translation that leverages theorem provers to verify semantic entailment rather than relying on superficial token overlap. By using positive and contrastive probes derived from target formulas, the method effectively penalizes logical errors like quantifier swaps that traditional metrics often miss. This advancement directly addresses a critical bottleneck in symbolic reasoning pipelines where accurate translation is prerequisite for valid inference.
Quizzing the Translation: A Prover-Grounded Evaluation Metric for NL$\rightarrow$FOL
arXiv:2609.33612v1 Announce Type: new Abstract: A standard pipeline for symbolic reasoning over natural-language problems translates them into first-order logic and invokes a theorem prover. The translation step is the bottleneck: swap "every" for "some" and every inference that follows is corrupted. Yet today's metrics often score more broken translations higher than less broken ones, because BLEU, BERTScore, and Smatch++ reward surface overlap that the worst errors happen to preserve. We introduce SIV, which derives two kinds of probes from the target formula and uses a theorem prover to verify the candidate translation against each. Positive probes are statements the candidate must entail, which detect translations that drop content; contrastive probes are statements the candidate must not entail, which detect translations that assert more than the original. On a controlled pool of perturbed FOLIO translations, the severity of the error accounts for 80% of SIV's score variance, compared with at most 17% for any prior metric. Across six error classes on a disjoint pool, SIV scores the reference above the perturbed candidate in over 99% of pairs. Because each probe is labeled with what it tests, the failure pattern also supplies a labeled error trace, recovering the perturbation class at macro-F1 0.638, nearly double the score-only baseline. On 434 expert-audited real LLM translations, SIV attains the top AUC, uniquely detects and grades expert-labeled major errors, and abstains, rather than mis-scoring, on out-of-vocabulary translations.
Abstract:A standard pipeline for symbolic reasoning over natural-language problems translates them into first-order logic and invokes a theorem prover. The translation step is the bottleneck: swap "every" for "some" and every inference that follows is corrupted. Yet today's metrics often score more broken translations higher than less broken ones, because BLEU, BERTScore, and Smatch++ reward surface overlap that the worst errors happen to preserve. We introduce SIV, which derives two kinds of probes from the target formula and uses a theorem prover to verify the candidate translation against each. Positive probes are statements the candidate must entail, which detect translations that drop content; contrastive probes are statements the candidate must not entail, which detect translations that assert more than the original. On a controlled pool of perturbed FOLIO translations, the severity of the error accounts for 80% of SIV's score variance, compared with at most 17% for any prior metric. Across six error classes on a disjoint pool, SIV scores the reference above the perturbed candidate in over 99% of pairs. Because each probe is labeled with what it tests, the failure pattern also supplies a labeled error trace, recovering the perturbation class at macro-F1 0.638, nearly double the score-only baseline. On 434 expert-audited real LLM translations, SIV attains the top AUC, uniquely detects and grades expert-labeled major errors, and abstains, rather than mis-scoring, on out-of-vocabulary translations.
Accepted to EMNLP 2026 (Main Conference). 18 pages, 3 figures, 10 tables. Code and data: this https URL
Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO)
arXiv:2609.33612 [cs.CL]
(or arXiv:2609.33612v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2609.33612 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 348 words
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