The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Other Variants of Math Problems <s> This paper presents intial work on a system that bridges from robust, broad-coverage natural language processing to precise semantics and automated reasoning, focusing on solving logic puzzles drawn from sources such as the Law School Admission Test (LSAT) and the analytic section of the Graduate Record Exam (GRE). We highlight key challenges, and discuss the representations and performance of the prototype system. <s> BIB001 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Other Variants of Math Problems <s> What capabilities are required for an AI system to pass standard 4th Grade Science Tests? Previous work has examined the use of Markov Logic Networks (MLNs) to represent the requisite background knowledge and interpret test questions, but did not improve upon an information retrieval (IR) baseline. In this paper, we describe an alternative approach that operates at three levels of representation and reasoning: information retrieval, corpus statistics, and simple inference over a semi-automatically constructed knowledge base, to achieve substantially improved results. We evaluate the methods on six years of unseen, unedited exam questions from the NY Regents Science Exam (using only non-diagram, multiple choice questions), and show that our overall system's score is 71.3%, an improvement of 23.8% (absolute) over the MLN-based method described in previous work. We conclude with a detailed analysis, illustrating the complementary strengths of each method in the ensemble. Our datasets are being released to enable further research. <s> BIB002 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Other Variants of Math Problems <s> Answering questions in a university's entrance examination like Gaokao in China challenges AI technology. As a preliminary attempt to take up this challenge, we focus on multiple-choice questions in Gaokao, and propose a three-stage approach that exploits and extends information retrieval techniques. Taking Wikipedia as the source of knowledge, our approach obtains knowledge relevant to a question by retrieving pages from Wikipedia via string matching and context-based disambiguation, and then ranks and filters pages using multiple strategies to draw critical evidence, based on which the truth of each option is assessed via relevance-based entailment. It achieves encouraging results on real-life questions in recent history tests, significantly outperforming baseline approaches. <s> BIB003 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Other Variants of Math Problems <s> Solving algebraic word problems requires executing a series of arithmetic operations---a program---to obtain a final answer. However, since programs can be arbitrarily complicated, inducing them directly from question-answer pairs is a formidable challenge. To make this task more feasible, we solve these problems by generating answer rationales, sequences of natural language and human-readable mathematical expressions that derive the final answer through a series of small steps. Although rationales do not explicitly specify programs, they provide a scaffolding for their structure via intermediate milestones. To evaluate our approach, we have created a new 100,000-sample dataset of questions, answers and rationales. Experimental results show that indirect supervision of program learning via answer rationales is a promising strategy for inducing arithmetic programs. <s> BIB004
Apart from geometric problems, there are also assorted variants of math problems that AI system focuses on. Aristo BIB002 is able to solve non-diagram multiple-choice questions through five parallel solvers, one for pure text, two for statistic and two for inference. Finally, the combiner of Aristo outputs a comprehensive score of each option based on scores from the five solvers. A similar work on multiple-choice questions is BIB003 , which takes Wikipedia as a knowledge base. After ranking and filtering relevant pages retrieved from Wikipedia, it presents a new scoring function to pick the best answer from the candidates. Another vairant is targeted at solving IQ test and a noticeable number of computer models have been proposed in  ,  . Taking  for example, it proposed a framework for solving verbal IQ questions, which classifies questions into several categories and each group of questions are solved by a specific solver respectively. Furthermore, logic puzzles are addressed in BIB001 by transforming robust natural language to precise semantics. For other forms of math problems,  solves probability problems automatically by a two-step approach, namely first formulating questions in a declarative language and then computing the answer through a solver implemented in ProbLog  . And algebraic word problems are solved by generating answer rationales written in natural language in BIB004 through a sequence-to-sequence model.