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.
Extensive efforts have been made in the domain of math problem solving @cite_14 @cite_16 @cite_0 , which aim at obtaining the correct answer to a given math problem. Other work has focused on learning to map math expressions into formal languages @cite_11 . We aim to generate natural language rationales, where the bindings between variables and the problem solving approach are mixed into a single generative model that attempts to solve the problem while explaining the approach taken.
@cite_0 @cite_14 @cite_16 @cite_11
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This paper presents a semantic parsing and reasoning approach to automatically solving math word problems. A new meaning representation language is designed to bridge natural language text and math expressions. A CFG parser is implemented based on 9,600 semi-automatically created grammar rules. We conduct experiments on a test set of over 1,500 number word problems (i.e., verbally expressed number problems) and yield 95.4 precision and 60.2 recall. Identifying mathematical relations expressed in text is essential to understanding a broad range of natural language text from election reports, to financial news, to sport commentaries to mathematical word problems. This paper focuses on identifying and understanding mathematical relations described within a single sentence. We introduce the problem of Equation Parsing -- given a sentence, identify noun phrases which represent variables, and generate the mathematical equation expressing the relation described in the sentence. We introduce the notion of projective equation parsing and provide an efficient algorithm to parse text to projective equations. Our system makes use of a high precision lexicon of mathematical expressions and a pipeline of structured predictors, and generates correct equations in @math of the cases. In @math of the time, it also identifies the correct noun phrase @math variables mapping, significantly outperforming baselines. We also release a new annotated dataset for task evaluation. 1. Summary In Part I, four ostensibly different theoretical models of induction are presented, in which the problem dealt with is the extrapolation of a very long sequence of symbols—presumably containing all of the information to be used in the induction. Almost all, if not all problems in induction can be put in this form. Some strong heuristic arguments have been obtained for the equivalence of the last three models. One of these models is equivalent to a Bayes formulation, in which a priori probabilities are assigned to sequences of symbols on the basis of the lengths of inputs to a universal Turing machine that are required to produce the sequence of interest as output. Though it seems likely, it is not certain whether the first of the four models is equivalent to the other three. Few rigorous results are presented. Informal investigations are made of the properties of these models. There are discussions of their consistency and meaningfulness, of their degree of independence of the exact nature of the Turing machine used, and of the accuracy of their predictions in comparison to those of other induction methods. In Part II these models are applied to the solution of three problems—prediction of the Bernoulli sequence, extrapolation of a certain kind of Markov chain, and the use of phrase structure grammars for induction. Though some approximations are used, the first of these problems is treated most rigorously. The result is Laplace's rule of succession. The solution to the second problem uses less certain approximations, but the properties of the solution that are discussed, are fairly independent of these approximations. The third application, using phrase structure grammars, is least exact of the three. First a formal solution is presented. Though it appears to have certain deficiencies, it is hoped that presentation of this admittedly inadequate model will suggest acceptable improvements in it. This formal solution is then applied in an approximate way to the determination of the “optimum” phrase structure grammar for a given set of strings. The results that are obtained are plausible, but subject to the uncertainties of the approximation used. Research has seen considerable achievements concerning translation of natural language patterns into formal queries for Question Answering (QA) based on Knowledge Graphs (KG). One of the main challenges in this research area is about how to identify which property within a Knowledge Graph matches the predicate found in a Natural Language (NL) relation. Current approaches for formal query generation attempt to resolve this problem mainly by first retrieving the named entity from the KG together with a list of its predicates, then filtering out one from all the predicates of the entity. We attempt an approach to directly match an NL predicate to KG properties that can be employed within QA pipelines. In this paper, we specify a systematic approach as well as providing a tool that can be employed to solve this task. Our approach models KB relations with their underlying parts of speech, we then enhance this with extra attributes obtained from Wordnet and Dependency parsing characteristics. From a question, we model a similar representation of query relations. We then define distance measurements between the query relation and the properties representations from the KG to identify which property is referred to by the relation within the query. We report substantive recall values and considerable precision from our evaluation.