# Mapping to Declarative Knowledge for Word Problem Solving

arXiv: https://arxiv.org/abs/1712.09391 · HTML: https://mlsanity.com/paper/1712.09391/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Dec 2017.

## Built on by (most cited first, 30 of 36)

- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [NumGLUE: A Suite of Fundamental yet Challenging Mathematical Reasoning Tasks](https://mlsanity.com/paper/2204.05660/) (2022)
- [State-of-the-art generalisation research in NLP: A taxonomy and review](https://mlsanity.com/paper/2210.03050/) (2022)
- [Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction](https://mlsanity.com/paper/2203.10316/) (2022)
- [Scalable Influence and Fact Tracing for Large Language Model Pretraining](https://mlsanity.com/paper/2410.17413/) (2024)
- [Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks](https://mlsanity.com/paper/2107.01431/) (2021)
- [Mathematical Language Models: A Survey](https://mlsanity.com/paper/2312.07622/) (2023)
- [NOAHQA: Numerical Reasoning with Interpretable Graph Question Answering Dataset](https://mlsanity.com/paper/2109.10604/) (2021)
- [Cutting Through the Noise: Boosting LLM Performance on Math Word Problems](https://mlsanity.com/paper/2406.15444/) (2024)
- [Multi-View Reasoning: Consistent Contrastive Learning for Math Word Problem](https://mlsanity.com/paper/2210.11694/) (2022)
- [Lila: A Unified Benchmark for Mathematical Reasoning](https://mlsanity.com/paper/2210.17517/) (2022)
- [Towards Tractable Mathematical Reasoning: Challenges, Strategies, and Opportunities for Solving Math Word Problems](https://mlsanity.com/paper/2111.05364/) (2021)
- [AI-Driven Virtual Teacher for Enhanced Educational Efficiency: Leveraging Large Pretrain Models for Autonomous Error Analysis and Correction](https://mlsanity.com/paper/2409.09403/) (2024)
- [A Survey on Mathematical Reasoning and Optimization with Large Language Models](https://mlsanity.com/paper/2503.17726/) (2025)
- [Sequence to General Tree: Knowledge-Guided Geometry Word Problem Solving](https://mlsanity.com/paper/2106.00990/) (2021)
- [World Models for Math Story Problems](https://mlsanity.com/paper/2306.04347/) (2023)
- [Why are NLP Models Fumbling at Elementary Math? A Survey of Deep Learning based Word Problem Solvers](https://mlsanity.com/paper/2205.15683/) (2022)
- [Fill in the Blank: Exploring and Enhancing LLM Capabilities for Backward Reasoning in Math Word Problems](https://mlsanity.com/paper/2310.01991/) (2023)
- [Solving for X and Beyond: Can Large Language Models Solve Complex Math Problems with More-Than-Two Unknowns?](https://mlsanity.com/paper/2407.05134/) (2024)
- [Generating Pedagogically Meaningful Visuals for Math Word Problems: A New Benchmark and Analysis of Text-to-Image Models](https://mlsanity.com/paper/2506.03735/) (2025)
- [From Correctness to Comprehension: AI Agents for Personalized Error Diagnosis in Education](https://mlsanity.com/paper/2502.13789/) (2025)
- [Language Modeling for the Future of Finance: A Survey into Metrics, Tasks, and Data Opportunities](https://mlsanity.com/paper/2504.07274/) (2025)
- [WARM: A Weakly (+Semi) Supervised Model for Solving Math word Problems](https://mlsanity.com/paper/2104.06722/) (2021)
- [ComSearch: Equation Searching with Combinatorial Strategy for Solving Math Word Problems with Weak Supervision](https://mlsanity.com/paper/2210.07017/) (2022)
- [Textual Enhanced Contrastive Learning for Solving Math Word Problems](https://mlsanity.com/paper/2211.16022/) (2022)
- [Multi-tool Integration Application for Math Reasoning Using Large Language Model](https://mlsanity.com/paper/2408.12148/) (2024)
- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)

## Abstract (arXiv)

Math word problems form a natural abstraction to a range of quantitative reasoning problems, such as understanding financial news, sports results, and casualties of war. Solving such problems requires the understanding of several mathematical concepts such as dimensional analysis, subset relationships, etc. In this paper, we develop declarative rules which govern the translation of natural language description of these concepts to math expressions. We then present a framework for incorporating such declarative knowledge into word problem solving. Our method learns to map arithmetic word problem text to math expressions, by learning to select the relevant declarative knowledge for each operation of the solution expression. This provides a way to handle multiple concepts in the same problem while, at the same time, support interpretability of the answer expression. Our method models the mapping to declarative knowledge as a latent variable, thus removing the need for expensive annotations. Experimental evaluation suggests that our domain knowledge based solver outperforms all other systems, and that it generalizes better in the realistic case where the training data it is exposed to is biased in a different way than the test data.