Research On Developing Algorithms For Solving Arithmetic Word Problems

Developing algorithms for solving math problems has been a challenging problem so that no widely applied algorithms are available after more than half a century of research.In the recent years,this research problem once again becomes an active research problem because two forces jointly motivate this research.One force is the huge demand for intelligent education and the other is the rapid progress wave of machine learning technology.Developing algorithms for solving math problems has long been a research problem in the field of artificial intelligence because this research has importance not only in theory but also in application of intelligent education.In theoretical aspect,this research involves multiple core research problems in various fields such as natural language processing,artificial intelligence,mathematics,and pedagoy.In addition to this,solving math problems is the basic abilbity of human beiing.In application aspect,automatic algorithms for solving math problems are the core technology of the educational intelligent tutoring system.The automatic algorithms for solving math problems can improve the intelligence level of the education tutorial system and enhance education balance among different areas by using educational technology.This dissertation focuses on developing algorithms for solving arithmetic word problems,which is a basic and challenging branch problem in developing algorithms for solving math problems.The problem is basic because arithmetic is the foundation of the whole mathematics and almost everyone needs to learn arithmetic.This problem is also challenging probably because the statement of arithmetic word problems is closest to the everyday language but not in the scientific form,which leads that understanding arithmetic word problems becomes a very difficult problem.The algorithms for solving arithmetic word problems usually can be divided into three steps:problem understanding,solving engine,and solution generation.The goal of problem understanding is to translate the problem text into a form that can be solved by existing methods.Traditional methods for understanding problems can be divided into two types,one based on semantic role analysis and the other based on machine learning.The method based on semantic role analysis has the disadvantage that the generalization ability is not strong.The lack of generalization ability is caused by the diversity of the same mathematical meanings expressed by natural language.The method of obtaining equations templates based on machine learning has the disadvantage of a limited number of target equations templates.In addition,both methods lack the function of discovering implicit mathematical relations.There were little efforts on establishing the theory of solving arithmetic word problems,which can be confirmed by the literature of this area,though some methods of solving arithmetic word problems have their own theory bases.To elevate the situation of less theory outcomes in problem solving,this dissertation establishes a relation principle of solving arithmetic word problems.The core ideas of this principle are the solving process can be viewed as the equavileant transform of relation groups and the problem understanding can be viewed as a process of acquiring a relation group from problem text that can represents the given problem in term of finding the solution.To overcome the demerit that the methods based on semantic analysis lack generalization ability,this dissertation proposes a syntactic and semantic model method to extract the direct explicit quantity relation from the problem text.Compared with the methods based on semantic analysis,the syntactic and semantic model method increases the use of syntactic information and reduces the reliance on the semantic information.The syntactic part of the syntactic and semantic model replaces the word combination of the traditional semantic role with the change pattern information of parts of speech.Therefore,the syntactic and semantic model increases the generalization ability of the model compared with the traditional methods.As a result,the new method needs a smaller number of new models than the traditional methods.When they are solving word problems,students sometimes need to add some relations according to their own knowledge to solve exercise problems.These relations are called implicit relations because they are not explicitly stated in problem text.Aiming at finding the implicit quantity relation from arithmetic word problems,this dissertation proposes a method to discover the implicit quantity relation in the arithmetic word problems by using machine learning tool.The machine learning based method predicts the type of implicit quantity relation required by arithmetic word problems through the features extracted from problem text and obtains the implicit quantity relation required for the solving engine by means of an implicit quantity relation knowledge base.For the quantity relation group obtained by the problem understanding through acquiring explicit and implicit relations from problem text,this dissertation proposes a method based on the process of automatic solution and the generation of readable solutions.This dissertation also proposes a method for transforming the solution process into a readable solution through semantic recovery.This dissertation prepares several sets of problems,as the test dataset.The experimental results on the dataset show that the proposed methods and algorithms are superior to the existaing ones.