@inproceedings{dong-etal-2026-rigor,
title = "{RIGOR}: Atomic Semantic Normalization and Declarative Constraint Reasoning for Geometry Problem Solving",
author = "Dong, Yuhang and
Yu, Weijie and
Wang, Ziheng and
Lv, Kunhang and
Han, Rui and
Jia, Fuqi and
Yin, Minghao and
Ma, Feifei",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.1385/",
pages = "31626--31642",
ISBN = "979-8-89176-459-0",
abstract = "Geometry Problem Solving (GPS) is a fundamental task in mathematical reasoning, with applications in intelligent education and automated theorem proving. Existing neuro-symbolic solvers often rely on two restrictive assumptions: textual conditions are expressed as atomic geometric statements, and target derivation can be reduced to eager elimination of intermediate variables. These assumptions break down in realistic problems, where coupled geometric descriptions lead to combinatorial growth in parsing patterns, and nonlinear constraints make explicit elimination inefficient or even intractable. We propose RIGOR, a neuro-symbolic GPS framework based on Atomic Semantic Normalization and Declarative Constraint Reasoning. RIGOR uses a Geometric Semantic Normalizer trained on our newly constructed GSN-15K dataset to normalize geometric texts into atomic statements for reliable formalization. It then adopts a Declarative Symbolic Engine that globally accumulates derived geometric constraints and determines target values through constraint entailment, while also reconstructing proof-grounded reasoning traces. Experiments on multiple standard GPS benchmarks show that RIGOR outperforms state-of-the-art methods while producing interpretable derivations. Our project is available at https://github.com/dongyuhang22/RIGOR."
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<abstract>Geometry Problem Solving (GPS) is a fundamental task in mathematical reasoning, with applications in intelligent education and automated theorem proving. Existing neuro-symbolic solvers often rely on two restrictive assumptions: textual conditions are expressed as atomic geometric statements, and target derivation can be reduced to eager elimination of intermediate variables. These assumptions break down in realistic problems, where coupled geometric descriptions lead to combinatorial growth in parsing patterns, and nonlinear constraints make explicit elimination inefficient or even intractable. We propose RIGOR, a neuro-symbolic GPS framework based on Atomic Semantic Normalization and Declarative Constraint Reasoning. RIGOR uses a Geometric Semantic Normalizer trained on our newly constructed GSN-15K dataset to normalize geometric texts into atomic statements for reliable formalization. It then adopts a Declarative Symbolic Engine that globally accumulates derived geometric constraints and determines target values through constraint entailment, while also reconstructing proof-grounded reasoning traces. Experiments on multiple standard GPS benchmarks show that RIGOR outperforms state-of-the-art methods while producing interpretable derivations. Our project is available at https://github.com/dongyuhang22/RIGOR.</abstract>
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%0 Conference Proceedings
%T RIGOR: Atomic Semantic Normalization and Declarative Constraint Reasoning for Geometry Problem Solving
%A Dong, Yuhang
%A Yu, Weijie
%A Wang, Ziheng
%A Lv, Kunhang
%A Han, Rui
%A Jia, Fuqi
%A Yin, Minghao
%A Ma, Feifei
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F dong-etal-2026-rigor
%X Geometry Problem Solving (GPS) is a fundamental task in mathematical reasoning, with applications in intelligent education and automated theorem proving. Existing neuro-symbolic solvers often rely on two restrictive assumptions: textual conditions are expressed as atomic geometric statements, and target derivation can be reduced to eager elimination of intermediate variables. These assumptions break down in realistic problems, where coupled geometric descriptions lead to combinatorial growth in parsing patterns, and nonlinear constraints make explicit elimination inefficient or even intractable. We propose RIGOR, a neuro-symbolic GPS framework based on Atomic Semantic Normalization and Declarative Constraint Reasoning. RIGOR uses a Geometric Semantic Normalizer trained on our newly constructed GSN-15K dataset to normalize geometric texts into atomic statements for reliable formalization. It then adopts a Declarative Symbolic Engine that globally accumulates derived geometric constraints and determines target values through constraint entailment, while also reconstructing proof-grounded reasoning traces. Experiments on multiple standard GPS benchmarks show that RIGOR outperforms state-of-the-art methods while producing interpretable derivations. Our project is available at https://github.com/dongyuhang22/RIGOR.
%U https://aclanthology.org/2026.emnlp-main.1385/
%P 31626-31642
Markdown (Informal)
[RIGOR: Atomic Semantic Normalization and Declarative Constraint Reasoning for Geometry Problem Solving](https://aclanthology.org/2026.emnlp-main.1385/) (Dong et al., EMNLP 2026)
ACL
- Yuhang Dong, Weijie Yu, Ziheng Wang, Kunhang Lv, Rui Han, Fuqi Jia, Minghao Yin, and Feifei Ma. 2026. RIGOR: Atomic Semantic Normalization and Declarative Constraint Reasoning for Geometry Problem Solving. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 31626–31642, Budapest, Hungary. Association for Computational Linguistics.