vericot-neuro-symbolic-chain-validation

name	vericot-neuro-symbolic-chain-validation
title	VeriCoT: Neuro-symbolic Chain-of-Thought Validation via Logical Consistency
version	0.0.2
engine	skillxiv-v0.0.2-claude-opus-4.6
license	MIT
url	https://arxiv.org/abs/2511.04662
keywords	["Chain-of-Thought","Formal Verification","Neuro-Symbolic AI","Logic Validation","LLM Reasoning"]
description	Validate LLM multi-step reasoning chains by converting natural language steps to first-order logic and checking logical consistency against established facts and sourced premises—enabling error detection and self-correction for more reliable reasoning.

Validate LLM Reasoning Through Logical Consistency Checking

Chain-of-Thought reasoning enables LLMs to decompose complex problems into justifiable steps. However, LLMs cannot reliably verify their own logic—flawed reasoning can produce correct-looking answers, creating false confidence. VeriCoT bridges this gap by combining neural language understanding with formal symbolic verification.

VeriCoT converts each reasoning step into first-order logic, identifies supporting premises from context or prior steps, and uses automated SMT solvers to verify logical validity. This neuro-symbolic approach exposes ungrounded claims, contradictions, and reasoning errors while maintaining human interpretability through natural language premises.

Core Concept

VeriCoT operates as a post-hoc verification system for Chain-of-Thought reasoning. Rather than modifying model architecture or training procedures, it validates completed reasoning traces by:

1. Formalizing reasoning - Converting natural language CoT steps into first-order logic (FOL) formulas
2. Identifying premises - Extracting grounding sources (context, commonsense, prior steps) that justify each step
3. Checking consistency - Using SMT solvers (Z3) to verify logical relationships between steps and premises
4. Classifying errors - Categorizing verification failures as ungrounded, contradictory, or untranslatable steps

Architecture Overview

• Autoformalization Module: LLM-driven two-stage translation from natural language to SMT-LIB FOL notation, iteratively extending variable declarations
• Premise Identification: Solicits supporting premises from source context, commonsense knowledge, or preceding reasoning steps
• Symbolic Verification: Z3 SMT solver checks three relationships: entailment (step logically follows), contradiction (step conflicts with facts), consistency (neither follows nor contradicts)
• Error Classification: Categorizes failures and computes verification scores across reasoning traces
• Downstream Integration: Routes verification signals to three enhancement pathways (inference-time reflection, supervised fine-tuning, preference optimization)

Implementation Steps

Step 1: Autoformalization Pipeline

Convert natural language CoT steps to first-order logic formulas. The LLM performs two-stage translation: initial formalization using existing variable declarations, then iterative extension of vocabulary (up to three iterations) if new concepts appear.

# Simplified formalization prompt structure
 ():
    
    
    prompt = 

    formula = llm_call(prompt)

    
    iteration = 
     iteration < max_iterations    formula.lower():
        prompt = 
        existing_declarations += llm_call(prompt)
        iteration += 

     formula