MATRIX AS PLAN: Structured Logical Reasoning with Feedback-Driven Replanning

TL;DR

MatrixCoT addresses the challenge of robust symbolic reasoning in LLMs by introducing a structured, solver-free pipeline that combines typed symbolic data management, a matrix-based reasoning plan, and a feedback-driven replanning mechanism. By representing dependencies in a binary matrix $A$ and enforcing topological execution, the approach preserves global relations among steps and exposes execution traces for auditable repairs. The four-module workflow—translator, matrix-based planner, solver, and replanner—produces verifiable, terminating reasoning trajectories without external solvers, yielding improved robustness and interpretability. Experimental results across five logical-reasoning benchmarks and five LLMs demonstrate competitive accuracy with substantially enhanced stability and transferability, highlighting practical impact for trustworthy web-scale reasoning systems.

Abstract

As knowledge and semantics on the web grow increasingly complex, enhancing Large Language Models (LLMs) comprehension and reasoning capabilities has become particularly important. Chain-of-Thought (CoT) prompting has been shown to enhance the reasoning capabilities of LLMs. However, it still falls short on logical reasoning tasks that rely on symbolic expressions and strict deductive rules. Neuro-symbolic methods address this gap by enforcing formal correctness through external solvers. Yet these solvers are highly format-sensitive, and small instabilities in model outputs can lead to frequent processing failures. LLM-driven approaches avoid parsing brittleness, but they lack structured representations and process-level error-correction mechanisms. To further enhance the logical reasoning capabilities of LLMs, we propose MatrixCoT, a structured CoT framework with a matrix-based plan. Specifically, we normalize and type natural language expressions, attach explicit citation fields, and introduce a matrix-based planning method to preserve global relations among steps. The plan becomes a verifiable artifact, making execution more stable. For verification, we also add a feedback-driven replanning mechanism. Under semantic-equivalence constraints, it identifies omissions and defects, rewrites and compresses the dependency matrix, and produces a more trustworthy final answer. Experiments on five logical-reasoning benchmarks and five LLMs show that, without relying on external solvers, MatrixCoT enhances both robustness and interpretability when tackling complex symbolic reasoning tasks, while maintaining competitive performance.

Figures (8)

• Figure 1: Illustration of Logical Reasoning with SymbCoT and the Proposed MatrixCoT. a) Structured vs. unstructured text representation. b) Ordinary plan vs. matrix-based plan.
• Figure 2: An overview of the MatrixCoT framework and methodology. The pipeline first translates the question into normalized, typed symbolic representations, then builds a matrix-based plan with dependencies and plan nodes. A problem solver executes the plan next, followed by a feedback-driven replanner to repair and re-execute the plan when needed. The system ultimately summarizes the information and extracts the answer.
• Figure 3: Ablation study. MP: Matrix-based plan; SRM: Structured data management; FDR: Feedback-Driven Replanner.
• Figure 4: Accuracy on ProofWriter as reasoning depth increases.
• Figure 5: Improvement from GPT– 4o-mini to GPT– 4o.