以「語言學理論」為基礎用「非機率模型」建立的數學應用問題作答系統

A Chinese Math Word Problem Solving System Based on Linguistic Theory and Non-statistical Approach

"本論文介紹一個基於語言學知識而非機率模型或類神經網路機器學習方法來實作的「中文數學應用問題解析」系統。一方面，該系統採納功能語言學學派（Functional Linguistics）的方法論，保存了「句式和意義（form and meaning）」之間的連結，將句型分類做為意圖偵測之用；另一方面，在逐步求解過程中，則採用形式語意學（Formal Semantics）的真值計算方式抽取事件結構中的論元（argument）詞彙。最後把與計算目標相關的論元取出後，傳給相應事件的函式進行數值計算。 和統計或機器學習方法相比，本論文提出的「功能-形式混合系統」不只具有極高的應用靈活性，亦能以相當少的資料進行訓練即可取得優良的意圖分類結果。使用本研究建立的模型，對國小一年級加減法及比較類的數學應用問題答題正確率達到99.29%。 本論文提出的中文數學應用問題解析系統除提供線上操作網頁外，亦將該系統的程式原始碼公開於Github專案頁面中。本論文主要貢獻如下：（1）提出一基於語言學知識解析自然語言中數學運算概念的方法與實作的系統；（2）以系統實作証明透過適當的中文斷詞處理及POS/ NER標記後，句型和意義之間的發散度可迅速收斂成為人類可閱讀並理解的邏輯表徵方式；（3）提供基於台灣小學數學課本中的數學應用問題而編寫的繁體中文測試題庫，並以MIT授權釋出。"

Aside from statistics based and NN machine learning based approaches, this paper presents a Chinese math word problem (CMWP) solving system that is implemented with linguistic reasons. On one hand, the system adopts the functional approach to keep the relation between form and meaning for intent detection. On the other hand, its argument extraction design follows how formal semantics calculate meanings of languages. The proposed system shows great flexibility with minimal training data requirement. When applying the model to 1st-year elementary level CMWP, the correct rate is between 98.57% and 99.29%. This paper also presents an adjustment procedure to reveal the potentials of the system to improve edging problems. The proposed hybrid system provides an operational webpage, its source codes are also accessible on Github.com. The main contributions of this paper are listed: (1) It implements a working system that is based on linguistic knowledge to solve CMWP. (2) The system proves that with proper Chinese word segmentation and POS/ NER tagging, the divergence between form and meaning can converge to a set of human-readable regular expressions. (3) The CMWP based on Taiwan elementary math textbooks are released under MIT license on Github.com.