VeriCoT: Neuro-Symbolic CoT Verification

• VeriCoT is a neuro-symbolic methodology that transforms natural language chain-of-thought reasoning into formal first-order logic for rigorous logical consistency verification.
• It employs a two-stage pipeline to auto-formalize each reasoning step into SMT-LIB compliant FOL formulas and checks entailment using automated theorem proving.
• The framework delivers real-time diagnostic signals for self-refinement and fine-tuning, enhancing trustworthiness in high-stakes domains like legal, biomedical, and scientific areas.

VeriCoT is a neuro-symbolic methodology for validating the logical consistency of Chain-of-Thought (CoT) reasoning produced by LLMs. Unlike approaches that focus solely on the content or surface accuracy of generated outputs, VeriCoT operates at the level of formal logical structure, automatically translating each natural-language reasoning step into a fragment of first-order logic (FOL) and verifying its entailment using automated theorem proving. This systematic pipeline supports step-wise assessment of logical validity, grounds each inference in explicit premises derived from context or commonsense, and provides diagnostic signals both for real-time model refinement and for enhanced fine-tuning regimes. The method addresses a critical gap in current LLM reasoning: even when final answers are correct, the underlying justification may be logically invalid or ungrounded, especially in settings where reliability and traceability are paramount.

1. Motivation and Challenges in CoT Verification

LLMs, when prompted with CoT, generate multi-step reasoning sequences (C₁, C₂, ..., Cₙ) that improve benchmark performance across diverse domains. However, a profound limitation is the absence of built-in mechanisms for verifying whether each individual step follows from the context, background knowledge, or prior reasoning, as required in legal, biomedical, or scientific settings. LLM-generated CoT can be “fluent but fallacious,” with invalid intermediate inferences remaining undetected when only the final answer is checked. Existing remedies such as post-hoc critics, program execution, or self-refinement are domain-limited or patch specific errors without addressing the general step-wise validity problem.

The core challenge is to develop a generic, rigorous method for the formal validation of each reasoning step in arbitrary domains, leveraging both machine-verifiable logical consistency and explicit tracing of inferential grounding—thereby offering both transparency and diagnostic capability for both models and users.

2. Formalization: Translating CoT Steps to First-Order Logic

VeriCoT introduces a two-stage pipeline for mapping each natural-language CoT step $\varphi_i(\vec{x})$ into a formal FOL formula $F_i$, adopting the SMT-LIB syntax compatible with state-of-the-art automated solvers (e.g., Z3). The translation proceeds as follows:

• Stage 1: Given the current logical vocabulary (declared sorts, constants, function/predicate symbols), the LLM is prompted to emit an SMT-LIB assertion corresponding to each CoT step. For example, the NL statement “Charlie is at most 18 years old in 2023” yields

  (<= (age charlie 2023) 18)

  leveraging application-specific symbols.
• Stage 2: If required symbols are missing, a secondary prompting step requests the LLM to extend the vocabulary (e.g., declaring age : Person × Int → Int), and retries auto-formalization up to three times before classifying as untranslatable.

VeriCoT encodes standard NL-to-FOL mapping rules:

• Conjunction (“and”) as and
• Disjunction (“or”) as or
• Negation as not
• Universal quantification (“for all”) and existential quantification (“there exists”) as forall and exists
• Implication as => Predicates map to uninterpreted functions/predicates in the FOL signature.

3. Premise Extraction and Step Grounding

For each CoT step, VeriCoT systematically identifies and encodes the premises required to ground its logical claim. Premises fall into three categories:

1. Source Context Premises: Explicit facts or rules provided in the question or accompanying document, e.g., regulatory clauses or problem assumptions.
2. Commonsense Knowledge: General axioms accepted in the relevant domain, such as age arithmetic or general scientific laws.
3. Prior Reasoning Steps: The sequence of FOL formulas corresponding to already verified CoT steps.

A premise pool $\mathcal{P} = \{P_1, P_2, ...\}$ is maintained, and each step’s FOL formula must be logically entailed by some combination of pool elements and previous step formulas. Steps that cannot be so justified are flagged as ungrounded.

Illustrative example (in FOL SMT-LIB syntax):

• Source context:

  (forall ((x Person)) (=> (and (< (age x 2023) 21) (exists ((y Person)) (and (livesWith x y) (parent y x)))) (Qualifies x) ) )

• Commonsense:

  (forall ((p Person) (y Int)) (<= (age p y) (- y (birthYear p))) )

4. Symbolic Consistency-Checking via Automated Reasoning

The symbolic verification phase operates as follows. For each step $i$:

1. Autoformalize: Map NL to FOL formula $F_i$, or flag as untranslatable.
2. Contradiction Check: Use Z3 to check if prior steps plus premises entail the negation of $F_i$, in which case the step is flagged “contradictory.”
3. Entailment Check: Use Z3 to determine if prior information entails $F_i$ directly.
4. Premise Generation: If direct entailment fails, the LLM is prompted to propose additional premises. Each candidate is translated and tested (joint consistency and entailment). If all attempts fail, the step is flagged “ungrounded.”

This pipeline returns, for each step, its formal translation, premise set, and error status (none/contradiction/ungrounded/untranslatable). The logical correctness criterion for a reasoning chain is thus: $$\mathcal{P} \cup \{F_1,\ldots,F_{i-1}\} \models F_i$$ for each $i$. All formal checks are conducted over a decidable FOL subset (linear arithmetic, uninterpreted functions, quantifiers).

5. Leveraging Verification Signals: Self-Reflection and Fine-Tuning

VeriCoT’s verification outputs provide structured feedback for multiple enhancement strategies:

A. Inference-Time Self-Reflection

For unverified CoTs (steps failing logical checks), the LLM is re-prompted with the original question, CoT, symbolic translations, premises, and solver verdicts for each step. The model is tasked to revise only those steps identified as ungrounded or contradictory. Empirically, this procedure increases the verification pass rate by +46% (relative) and verified correct answer rate by +41% relative, averaged across ProofWriter, LegalBench-SARA, and BioASQ.

B. Supervised Fine-Tuning (SFT)

A distillation process filters for (question, verified CoT, answer) triples where all CoT steps pass VeriCoT checks, optionally subject to an LLM-based premise plausibility check. Fine-tuning on this dataset improves task accuracy by +3% absolute on BioASQ (77.4%→79.7%) and ProofWriter (47.5%→51.1%) compared to conventionally filtered CoTs.

C. Preference Fine-Tuning with DPO

Pairs of (verified, unverified) CoTs for each question are constructed, and Direct Preference Optimization (DPO) is applied to incentivize higher model likelihood for logically verified chains. The DPO objective is: $$L_{\mathrm{DPO}}(\theta) = \mathbb{E}_{(x,c^{+},c^{-})} [ -\log \sigma(\Delta\pi) + \lambda\|\theta-\theta_{\mathrm{ref}}\|^2 ]$$ where $$\Delta\pi = \log\pi_\theta(c^+|x) - \log\pi_\theta(c^-|x)$$. Applying DPO on top of SFT further boosts pass rate by +18% (relative) and verified answer rate by +17.7% relative.

6. Experimental Evaluation and Results

VeriCoT is evaluated on three benchmarks:

• ProofWriter: Logical proof tasks requiring compositional, multi-step logical deduction.
• LegalBench-SARA: Statutory tax law reasoning with high domain complexity.
• BioASQ: Biomedical QA requiring fact synthesis from PubMed abstracts.

Key metrics reported:

• Verification Pass Rate: Proportion of CoTs with all steps verified.
• Verifier Precision: Among verified CoTs, fraction with correct final answers.
• Verified Correct Answer Rate (VCAR): Product of pass rate and precision.
• Task Accuracy: Overall proportion of correct answers.

Baseline comparisons show that VeriCoT achieves superior verification pass rate (45.2% vs. 14.8% on ProofWriter) and VCAR, while maintaining >94% precision. The addition of self-reflection and fine-tuning further amplifies these gains with little or no precision loss.

7. Broader Implications, Limitations, and Outlook

VeriCoT delivers a unified, end-to-end approach for rigorous validation of LLM-generated reasoning. Its explicit auto-formalization and grounding mechanisms make logical flaws and unsupported inference steps transparent to both users and downstream systems, enabling new modes of model assessment and trustworthy deployment. Notable implications include:

• Diagnostics: Provides actionable, step-local error signals rather than black-box outputs.
• Training: Shapes data collection towards CoTs with machine-verifiable logical fidelity.
• Trust: Raises the standard for LLM explanations in high-stakes domains.

Limitations include the reliance on LLMs’ ability to accurately auto-formalize NL into FOL (untranslatable steps), and the theoretical fragment supported by the underlying SMT solver. A plausible implication is that advancing language-to-logic models and hybrid neuro-symbolic interfaces could expand both the scope and accuracy of such frameworks.

In summary, VeriCoT establishes a practical and principled methodology for validating LLM reasoning at scale, making logical verification a first-class citizen in neuro-symbolic machine intelligence (Feng et al., 6 Nov 2025).