The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Statistic-based Methods <s> “Meaning” may be assigned to a string in a context-free language by defining “attributes” of the symbols in a derivation tree for that string. The attributes can be defined by functions associated with each production in the grammar. This paper examines the implications of this process when some of the attributes are “synthesized”, i.e., defined solely in terms of attributes of thedescendants of the corresponding nonterminal symbol, while other attributes are “inherited”, i.e., defined in terms of attributes of theancestors of the nonterminal symbol. An algorithm is given which detects when such semantic rules could possibly lead to circular definition of some attributes. An example is given of a simple programming language defined with both inherited and synthesized attributes, and the method of definition is compared to other techniques for formal specification of semantics which have appeared in the literature. <s> BIB001 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Statistic-based Methods <s> Understanding of free-format multi-step arithmetic word problems with extraneous information is discussed. A model including a full set of general skills necessary for understanding such problems was developed and computer implemented. The validity of the simulation was confirmed by testing on a variety of word problems with extraneous information. The results of this study show the way for moving from an intuitive understanding of word problems to a conscious and controlled process. <s> BIB002 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Statistic-based Methods <s> This paper presents a novel approach to learning to solve simple arithmetic word problems. Our system, ARIS, analyzes each of the sentences in the problem statement to identify the relevant variables and their values. ARIS then maps this information into an equation that represents the problem, and enables its (trivial) solution as shown in Figure 1. The paper analyzes the arithmetic-word problems “genre”, identifying seven categories of verbs used in such problems. ARIS learns to categorize verbs with 81.2% accuracy, and is able to solve 77.7% of the problems in a corpus of standard primary school test questions. We report the first learning results on this task without reliance on predefined templates and make our data publicly available. 1 <s> BIB003 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Statistic-based Methods <s> Little work from the Natural Language Processing community has targeted the role of quantities in Natural Language Understanding. This paper takes some key steps towards facilitating reasoning about quantities expressed in natural language. We investigate two different tasks of numerical reasoning. First, we consider Quantity Entailment, a new task formulated to understand the role of quantities in general textual inference tasks. Second, we consider the problem of automatically understanding and solving elementary school math word problems. In order to address these quantitative reasoning problems we first develop a computational approach which we show to successfully recognize and normalize textual expressions of quantities. We then use these capabilities to further develop algorithms to assist reasoning in the context of the aforementioned tasks. <s> BIB004 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Statistic-based Methods <s> This paper describes our system which solves simple arithmetic word problems. The system takes a word problem described in natural language, extracts information required for representation, orders the facts presented, applies procedures and derives the answer. It then displays this answer in natural language. The emphasis of this paper is on the natural language processing(NLP) techniques used to retrieve the relevant information from the English word problem. The system shows improvements over existing systems. <s> BIB005 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Statistic-based Methods <s> Solving simple arithmetic word problems is one of the challenges in Natural Language Understanding. This paper presents a novel method to learn to use formulas to solve simple arithmetic word problems. Our system, analyzes each of the sentences to identify the variables and their attributes; and automatically maps this information into a higher level representation. It then uses that representation to recognize the presence of a formula along with its associated variables. An equation is then generated from the formal description of the formula. In the training phase, it learns to score the pair from the systematically generated higher level representation. It is able to solve 86.07% of the problems in a corpus of standard primary school test questions and beats the state-of-the-art by <s> BIB006 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Statistic-based Methods <s> This demonstration presents a tag-based statistical English math word problem (MWP) solver with understanding, reasoning, and explanation. It analyzes the text and transforms both body and question parts into their tag-based logic forms, and then performs inference on them. The proposed tag (e.g., Agent, Verb, etc.) provides the flexibility for annotating an extracted math quantity with its associated syntactic and semantic information, which can be used to identify the desired operand and filter out irrelevant quantities (so that the answer can be obtained precisely). Since the physical meaning of each quantity is explicitly represented with those tags and used in the inference process, the proposed approach could explain how the answer is obtained in a human comprehensible way. <s> BIB007
The statistic-based methods leverage traditional machine learning models to identify the entities, quantities and operators from the problem text and yield the numeric answer with simple logic inference procedure. The scheme of quantity entailment proposed in BIB004 can be used to solve arithmetic problems with only one operator. It involves three types of classifiers to detect different properties of the word problem. The quantity pair classifier is trained to determine which pair of quantities would be used to derive the answer. The operator classifier picks the operator op ∈ {+, −, ×, ÷} with the highest probability. The order classifier is relevant only for problems involving subtraction or division because the order of operands matters for these two types of operators. With the inferred expression, it is straightforward to calculate the numeric answer for the simple math problem. To solve math problems with multi-step arithmetic expression, the statistic-based methods require more advanced logic templates. This usually incurs additional overhead to annotate the text problems and associate them with the introduced template. As an early attempt, ARIS BIB003 defines a logic template named state that consists of a set of entities, their containers, attributes, quantities and relations. For example, "Liz has 9 black kittens" initializes the number of kitten (referring to an entity) with black color (referring to an attribute) and belonging to Liz (referring to a container). The solution splits the problem text into fragments and tracks the update of the states by verb categorization. More specifically, the verbs are classified into seven categories: observation, positive, negative, positive transfer, negative transfer, construct and destroy. To train such a classifier, we need to annotate each split fragment in the training dataset with the associated verb category. Another drawback of ARIS is that it only supports addition and subtraction. BIB005 follows a similar processing logic to ARIS. It predefines a corpus of logic representation named schema, inspired by BIB002 . The sentences in the text problem are examined sequentially until the sentence matches a schema, triggering an update operation to modify the number associated with the entities. In BIB006 , Mitra et al. proposed a new logic template named formula. Three types of formulas are defined, including part whole, change and comparison, to solve problems with addition and subtraction operators. For example, the text problem "Dan grew 42 turnips and 38 cantelopes. Jessica grew 47 turnips. How many turnips did they grow in total?" is annotated with the partwhole template: whole : x, parts : {42, 47} . To solve a math problem, the first step connects the assertions to the formulas. In the second step, the most probable formula is identified using the log-linear model with learned parameters and converted into an algebraic equation. Another type of annotation is introduced in  , BIB007 to facilitate solving a math problem. A group of logic forms are predefined and the problem text is converted into the logic form representation by certain mapping rules. For instance, the sentence "Fred picks 36 limes" will be transformed into verb BIB001 . Finally, logic inference is performed on the derived logic statements to obtain the answer. To sum up, these statistical-based methods have two drawbacks that limit their usability. First, it requires additional annotation overhead that prevents them from handling large-scale datasets. Second, these methods are essentially based on a set of pre-defined templates, which are brittle and rigid. It will take great efforts to extend the templates to support other operators like multiplication and division. It is also not robust to diversified datasets. In the following, we will introduce the tree-based solutions, which are widely adopted and become the mainstreaming solutions to arithmetic word problems.