自然語言處理中的問答問題是一項極具挑戰性的任務。這類型的任務需要先了解使用者的文字輸入，再生成正確的文字輸出，過程包含了文意理解和文章生成任務。其中，數學應用問題解題更是需要具備使用公式做計算的能力。本論文建立了一台灣小學幾何問題的解題演算法，可以回答以自然語言寫成的數學題目。我們的作法包含三部分：意圖分類、讀題，以及解題。我們先透過文本分類，判斷題目中每句話的意圖。再根據意圖從句子中擷取資訊，建立容納這些資訊的表單。最後，根據表單的資訊，運用公式進行解題。除了解題之外，我們的解題器還提供計算過程和題型分類，以便讓使用者更容易理解題目。

本篇論文貢獻有三：一，利用語法規則和語意依存分析取代需要大量資料的深度學習模型，大幅減少對訓練資料數目的依賴性；二，建立了一台灣小學幾何問題資料集，包含題目敘述、正確解答，以及意圖標註；三，在極少的訓練資料下，完成了一個數學應用問題解題器，並達到了 81.7% 的解題正確率。

In Natural Language Processing, question answering is a challenging task. Such task requires understanding of user input, and generating the appropriate response, which involves natural language understanding and text generation. Among all types of questions, solving math word problems (MWP) requires utilizing formulas for calculating the correct answer. In this thesis, we propose an algorithm specifically designed to solve mathematical word problems (MWP) in the domain of elementary-level geometry in Taiwan. Our approach consists of three parts: intent classification, problem comprehension, and problem solving. We determine the intent of each sentence in the question by text classification. Then, based on the intents, we extract information from the sentences and construct a form to accommodate this information. Finally, we utilize formulas to solve the input problem based on the information in the forms. In addition to problem solving, our problem solver also provides computation process and problem type classification, facilitating users to better understand the questions.

The contribution of this thesis is in three-fold: First, we leverage regular expressions as a replacement for data-intensive deep learning models, which significantly reduce the reliance on a large scale datasets. Second, we establish a dataset for Taiwanese elementary school geometry problems, including problem descriptions, the correct answers, and annotations of intent for each sentence. Third, with minimal training data, we have developed a MWP solver that achieves an accuracy of 81.7%.

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