Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning

Lu, Pan; Gong, Ran; Jiang, Shibiao; Qiu, Liang; Huang, Siyuan; Liang, Xiaodan; Zhu, Song‐Chun

doi:10.18653/v1/2021.acl-long.528

Cited by 46 publications

(35 citation statements)

References 29 publications

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“…Geometry problem solving has been gaining more attention in the NLP community recently. Several geometry formal systems and datasets have been constructed, such as Geometry3K [29], GeoQA [6], GeometryQA [42]. Geometry3K translates the known conditions of geometric problems into formal statements, defining theorems as a set of rules for converting between formal statements.…”

Section: Related Workmentioning

confidence: 99%

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School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

Zhuang

Huang

et al. 2019

Mathematical Biosciences and Engineering

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The crystallization kinetics and melting behavior of nylon 10,10 in neat nylon 10,10 and in nylon 10,10 -montmorillonite (MMT) nanocomposites were systematically investigated by differential scanning calorimetry. The crystallization kinetics results show that the addition of MMT facilitated the crystallization of nylon 10,10 as a heterophase nucleating agent; however, when the content of MMT was high, the physical hindrance of MMT layers to the motion of nylon 10,10 chains retarded the crystallization of nylon 10,10, which was also confirmed by polarized optical microscopy. However, both nylon 10,10 and nylon 10,10 -MMT nanocomposites exhibited multiple melting be-havior under isothermal and nonisothermal crystallization conditions. The temperature of the lower melting peak (peak I) was independent of MMT content and almost remained constant; however, the temperature of the highest melting peak (peak II) decreased with increasing MMT content due to the physical hindrance of MMT layers to the motion of nylon 10,10 chains.

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Section: Related Workmentioning

confidence: 99%

“…1. The symbolic approaches [18] parse the images and texts of geometric problems into a unified formal language description, and then apply a predefined set of theorems to solve the problems. These approaches require the establishment of a formal system and the problem-solving process has mathematical rigor and good readability.…”

Section: Apply Theorem Timentioning

confidence: 99%

School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

Zhuang

Huang

et al. 2019

Mathematical Biosciences and Engineering

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“…For synthetic reasoning, geometric definitions and theorems are built inside machines, which then incorporate search techniques, often exhaustive, to find the solution [7]. Examples of the synthetic approach can be found in Inter-GPS [20] and GEOS [8], which are solvers with built-in Euclidean formulas. However, the algebraic approach has many limitations, and no geometric construction solver has adopted this method thus far.…”

Section: Computational Geometrymentioning

confidence: 99%

EuclidNet: Deep Visual Reasoning for Constructible Problems in Geometry

Wong¹,

Qi²,

Tan³

2023

Preprint

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In this paper, we present a deep learning-based framework for solving geometric construction problems through visual reasoning, which is useful for automated geometry theorem proving. Constructible problems in geometry often ask for the sequence of straightedge-and-compass constructions to construct a given goal given some initial setup. Our EuclidNet framework leverages the neural network architecture Mask R-CNN to extract the visual features from the initial setup and goal configuration with extra points of intersection, and then generate possible construction steps as intermediary data models that are used as feedback in the training process for further refinement of the construction step sequence. This process is repeated recursively until either a solution is found, in which case we backtrack the path for a step-by-step construction guide, or the problem is identified as unsolvable. Our EuclidNet framework is validated on complex Japanese Sangaku geometry problems, demonstrating its capacity to leverage backtracking for deep visual reasoning of challenging problems.

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“…For synthetic reasoning, geometric definitions and theorems are built inside machines, which then incorporate search techniques, often exhaustive, to find the solution [7]. Examples of the synthetic approach can be found in Inter-GPS [18] and GEOS [8], which are solvers with built-in Euclidean formulas. The algebraic approach involves algebraic operations such as Wenjun Wu's method [19] that decomposes problems based on the well-ordering principle and successive pseudo-reduction.…”

Section: Automated Geometric Reasoning With Formal Reasoningmentioning

confidence: 99%

EuclidNet: Deep Visual Reasoning for Constructible Problems in Geometry

Wong¹,

Qi²,

Tan³

2023

AAIML

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In this paper, we present a visual reasoning framework driven by deep learning for solving constructible problems in geometry that is useful for automated geometry theorem proving. Constructible problems in geometry often ask for the sequence of straightedge-and-compass constructions to construct a given goal given some initial setup. Our EuclidNet framework leverages the neural network architecture Mask R-CNN to extract the visual features from the initial setup and goal configuration with extra points of intersection, and then generate possible construction steps as intermediary data models that are used as feedback in the training process for further refinement of the construction step sequence. This process is repeated recursively until either a solution is found, in which case we backtrack the path for a step-by-step construction guide, or the problem is identified as unsolvable. Our EuclidNet framework is validated on the problem set of Euclidea with an average of 75% accuracy without prior knowledge and complex Japanese Sangaku geometry problems, demonstrating its capacity to leverage backtracking for deep visual reasoning of challenging problems.

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Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning

Cited by 46 publications

References 29 publications

School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

EuclidNet: Deep Visual Reasoning for Constructible Problems in Geometry

EuclidNet: Deep Visual Reasoning for Constructible Problems in Geometry

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