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.

机器阅读理解任务要求机器根据篇章文本回答相关问题。本文以抽取式机器阅读理解为例,重点考察当问题的线索要素与答案在篇章文本中跨越多个标点句时的阅读理解问题。本文将小句复合体结构自动分析任务与机器阅读理解任务融合,利用小句复合体中跨标点句话头札话体共享关系,来化简机器阅读理解任务的难度;并设计与实现了基于小句复合体的机器阅读理解模型。实验结果表明:在问题线索要素与答案跨越多个标点句时,答案抽取的精确匹配率(EM)相对于基准模型提升了3.49%,模型整体的精确匹配率提升了3.26%。