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Autonomous Evaluation of LLMs for Truth Maintenance and Reasoning Tasks
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Introduces AutoEval, a grammar-based, auto-generated benchmark that measures LLM truth maintenance across informalization and autoformalization of logic and regex, with formal verifiers (Prover9) checking equivalence, and shows its scores predict performance on other logic and translation benchmarks.
Problem
Benchmarks for LLM truth maintenance in formal-language translation and reasoning are static (contamination-prone), rely on BLEU-like metrics or human annotation, and cannot be easily updated for newer LLMs.
Approach
Compose informalization and autoformalization using the same LLM (FL -> NL -> FL) on CFG-generated formulas and check semantic equivalence of the round-trip output with a formal verifier, avoiding human labels and NL-side evaluation; also defines a predictive-power metric between benchmarks.
Key results
- For logic expressions with more than 20 operators, no evaluated LLM exceeded 50% truth maintenance accuracy in the round-trip.
- Calibrated AutoEval score shows strong positive correlation (rho >= 0.7) with other FL-based static benchmarks such as FOLIO; FOL LogiEval shows moderate correlation (0.5 to 0.7).
- Even SOTA large reasoning models (o1, DeepSeek-R1) fail to maintain truth effectively on a ~400-string subset.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| increase formal-expression complexity | Evaluated LLMs on AutoEval · AutoEval formal-language datasets | truth-maintenance accuracy | Hurt |
| use logic expressions with more than 20 operators | Evaluated LLMs · Logic | truth-maintenance accuracy | Hurt |
| increase expression complexity | LLMs acting as equivalence verifiers, even with CoT prompting · Formal-language expressions | F1 | Hurt |
| use an imbalanced, easier FOL evaluation set | AutoEval predictive power · LogiEval FOL | correlation: 0.5 ≤ ρ < 0.7 | Hurt |
| insert a negation into the translated natural-language sentence | BLEU · Weather-status translation example | BLEU: BLEU(ψ', ψ) = 0.74 (BLEU(ψ, ψ) = 1) | Hurt |
Surprising findings
- GPT-4o was less syntactically compliant on regex than the much smaller Phi and Llama-3 models, due to repeating token sequences until the token limit.
- LLMs struggle to verify logical equivalence even with chain-of-thought beyond toy expressions, with F1 falling sharply, and have difficulty with negations.
Limitations
- Equivalence for first-order logic is undecidable; a timeout was used and 0.66% of results timed out.
- Truth-maintenance evaluation covers only formal-language translation tasks such as logic and regex, not natural-language or image domains.
- Results for paid APIs depend on checkpoint availability, and pass@1 with a single sample is reported due to cost.
Experimental setup
Datasets: 3-CNF(12) PL(12) FOL(8,12)-S FOL(8,12)-E RE(2) FOLIO LogiEval HumanEval Big Bench Hard
Benchmarks: AutoEval FOLIO LogiEval HumanEval Big Bench Hard
Metrics: syntactic compliance rate truth maintenance score (pass@1) F1 for LLM verifier predictive power correlation with other benchmarks
Baselines: FOLIO LogiEval HumanEval Big Bench Hard BLEU
Builds on: Chain-of-thought FOLIO HumanEval Prover9
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