Knowledge-Centered Dual-Process Reasoning for Math Word Problems With Large Language Models - Research on KNOS and EKNOS Framework

Aug 23, 2026

Math word problem (MWP) evaluation tests both text understanding and mathematical knowledge mastery in AI models. Although large language models (LLMs) achieve strong results, they still frequently produce logical errors due to insufficient step-by-step knowledge-grounded reasoning. This paper introduces a Knowledge-guided Solver (KNOS) using dual-process cooperation: a knowledge system for invoking relevant knowledge and an inference system with verification and injection to guide interpretable symbolic deduction. An open-book variant, EKNOS, adds knowledge selectors to extract commonsense and formulas each step. Experiments on GPT3, ChatGPT, and GPT4 show improved reasoning accuracy.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages15

Reading Time38 min

AccessFree to download

Introduction

Problem and limitations of current LLM reasoning

Dual-process motivation

Proposed framework: KNOS

Knowledge system and knowledge invoker

Inference system: knowledge verifier and injector

Open-book extension: EKNOS

Knowledge selectors from external sources

Step-wise enhancement of reasoning

Experiments

GPT3, ChatGPT, GPT4 evaluation

Accuracy improvements and analysis

Knowledge-Centered Dual-Process Reasoning for Math Word Problems With Large Language Models Jiayu Liu , Zhenya Huang , Member, IEEE, Qi Liu, Member, IEEE, Zhiyuan Ma, Chengxiang Zhai, and Enhong Chen , Fellow, IEEE Abstract—Math word problem (MWP) serves as a critical milestone for assessing the text mining ability and knowledge mastery level of models. Recent advancements have witnessed large language models (LLMs) showcasing remarkable performance on MWP. However, current LLMs still frequently exhibit logical errors, which highlights their inability to fully grasp the knowledge required for genuine step-by-step mathematical reasoning. To this end, in this paper, we propose a novel Knowledge-guided Solver (KNOS) framework that empowers LLMs to simulate human mathematical reasoning, whose core idea is to Invoke-Verify-Inject necessary knowledge to solve MWP. We draw inspiration from the dual-process theory to construct two cooperative systems: a Knowledge System and an Inference System. Speciﬁcally, the Knowledge System employs LLMs as the knowledge base and develops a novel knowledge invoker that can elicit their relevant knowledge to support the strict step-level mathematical reasoning. In the Inference System, we propose a knowledge veriﬁer and a knowledge injector to evaluate the knowledge rationality and further guide the step-wise symbolic deduction in an interpretable manner based on human cognitive mechanism, respectively. Moreover, to tackle the potential scarcity issue of mathematics-speciﬁc knowledge in LLMs, we consider an open-book exam scenario and propose an improved version of KNOS called EKNOS. In EKNOS, we meticulously designknowledgeselectors to extract the most relevant commonsense and math formulas from external knowledge sources for each reasoning step. This knowledge is utilized to assist the knowledge invoker in better stimulating LLMs’ reasoning abilities. Both KNOS and EKNOS are ﬂexible to empower different LLMs. Our experiments with GPT3, ChatGPT, and GPT4 not only demonstrate their reasoning accuracy improvement but also show Received 14 June 2024; revised 7 March 2025; accepted 22 March 2025 . Date of publication 1 April 2025; date of current version 1 May 2025 . This research was partially supported in part by the National Key Research and Development Program of China under Grant 2021YFF0901005, in part by the Key Technologies R&D Program of Anhui Province under Grant 202423k09020039, in part by the National Natural Science Foundation of China under Grant 62477044 and Grant 62337001, and in part by the Fundamental Research Funds for the Central Universities under Grant WK2150110038 . The work of Zhenya Huang was supported by the Young Elite Scientists Sponsorship Program by CAST under Grant 2024QNRC001. Recommended for acceptance by W. Ding.(Corresponding author: Zhenya Huang.) Jiayu Liu and Qi Liu are with the School ofData Science, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei 230000, China (e-mail: [jy251198@mail.ustc.edu.cn](jy251198@mail.ustc.edu.cn); [qiliuql@ustc.edu.cn](qiliuql@ustc.edu.cn)). Zhenya Huang, Zhiyuan Ma, and Enhong Chen are with the School of Computer Science and Technology, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei 230000, China (e-mail: [huangzhy@ustc.edu.cn](huangzhy@ustc.edu.cn); [zhyma@mail.ustc.edu.cn](zhyma@mail.ustc.edu.cn); [cheneh@ustc.edu.cn](cheneh@ustc.edu.cn)). Chengxiang Zhai is with the Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, IL 61820 USA (e-mail: [czhai@illinois.edu](czhai@illinois.edu)) . This article has supplementary downloadable material available at [https://doi.org/10.1109/TKDE.2025.3556367](https://doi.org/10.1109/TKDE.2025.3556367), provided by the authors. Digital Object Identiﬁer 10.1109/TKDE.2025.3556367 how they bring the strict step-wise interpretability of mathematica

FAQs

What problem does the paper address in LLM-based math word problem solving?

LLMs often generate logical errors and reasoning steps that are not fully grounded in the needed mathematical knowledge, even when they produce step-by-step chains.

How does KNOS improve step-by-step mathematical reasoning?

KNOS uses an Invoke-Verify-Inject mechanism: it invokes relevant knowledge, verifies its rationality, and injects it to guide symbolic deduction in an interpretable way.

What additional capability does EKNOS add to handle limited math-specific knowledge in LLMs?

EKNOS assumes an open-book setting and designs knowledge selectors to extract the most relevant commonsense and math formulas from external sources for each reasoning step.

Aug 23, 2026

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