Combings of groups and the grammar of reparameterization

A new construction of combings is used to distinguish between several previously indistinguishable classes of groups associated to the theory of automatic groups and non-positive curvature in group theory. We construct synchronously bounded combings for a class of groups that are neither bicombable nor automatic. The linguistic complexity of these combings is analysed: in many cases the language of words in the combing is an indexed language.     

Quantitative analysis with linguistic values

The concept of quantitative analysis with linguistic values is set out and discussed. An APL-implemented auxiliary language is presented which makes such analysis operational with regard to humanistic systems where the variables cannot easily be numerically measured. Special emphasis is placed on linguistic approximation which is implemented by an APL-function of 19 statements with a range of approximately 10¹⁰ linguistic values. Examples of the linguistic input-linguistic output characteristics of the language are shown.     

The implementation of Fprolog—A fuzzy Prolog interpreter

Prolog, a programming language based on the first order predicate calculus, has been widely used in artificial intelligence research. One of its shortcomings is the lack of a natural mechanism to deal with uncertainty.A possible solution to this problem, outlined here, is to base Prolog on fuzzy logic rather than on conventional two-valued logic. This leads to a more general system, of which standard Prolog is a special case. To give the system greater flexibility, the fuzzy Prolog interpreter can link with the Fril system developed at Bristol, yielding a powerful language with breadth-first and depth-first search capabilities.     

不完全语言信息下的多准则群决策方法研究

针对决策者所给的自然语言信息缺失判断矩阵,提出了一种基于群体满意度最大的不完全语言信息多准则群决策规划模型.首先分析决策者所给的多准则语言评价信息矩阵,进而通过三角模糊数将多准则语言评价信息矩阵转化为三角模糊数矩阵;其次根据满意度函数构建不完全语言信息多准则群决策规划模型;最后通过实例验证本方法的可行性及有效性.实例表明该方法计算简单,易操作.     

Developing teacher capacity to explore non-routine problems through a focus on the social semiotics of mathematics classroom discourse

This paper reports on a research project exploring the social semiotics of mathematics teaching and learning in urban middle schools. Participating teachers attended a Lesson Study Group that focused on the linguistic and diagrammatic challenges of framing and solving non-routine mathematics problems. This paper describes key social semiotic concepts explored with the teachers during the lesson study activities, focusing on the complex conjunction of the mathematics register and everyday language. We use examples from the participants’ classrooms to show the relevance of these concepts in studying classroom discourse, focusing in particular on the complex conjunction of diagramming and language.     

Centripetal and centrifugal language forces in one elementary school second language mathematics classroom

Research on the learning and teaching of mathematics in contexts of language diversity has highlighted a number of common tensions that arise in a variety of contexts. These tensions can be explained by Bakhtin’s characterization of two sets of forces that are present in any utterance: centripetal forces represent the drive for unitary language, standardisation and linguistic hegemony; centrifugal forces represent the presence of heteroglossia, stratification and decentralisation. In this paper, I use this theoretical perspective to examine ethnographic data from a study of a second language mathematics classroom in Canada, in which the students are almost all speakers of Cree, one of the original languages of Canada. My analysis highlights three situations in which the tension between centripetal and centrifugal forces is particularly salient: the students’ use of Cree; working on mathematical word problems; and producing mathematical explanations.     

Integration of fuzzy linguistic information in language comprehension

To successfully understand a natural language utterance, a person must simultaneously consider information about its perceptual, syntactic, semantic, and pragmatic structure. At each of these levels of analysis, the linguistic information is continuously but systematically variable. It is argued that in order to cope with and, in fact, exploit this continuous information requires fuzzy propositional representations of linguistic knowledge. Such a fuzzy propositional theoretical framework is proposed and models of several specific language processing components are developed and empirically evaluated within this framework. The model system incorporates many of the major principles of current cognitive psychological theory and extends them into the fuzzy domain.     

方案有类别偏好的多粒度语言灰靶决策方法

研究了方案有类别偏好的不同粒度语言信息决策方法。基于不同粒度语言的距离转换函数方法,将其转换成标准语言距离;针对不完全的属性权重信息,通过灰靶决策的原理表征方案的综合靶心距;基于案例学习的思想,建立了考虑方案有多种类别偏好的属性权重确定模型。算例表明了方法有效性。     

A host system for integration of the components of a linguistic processor: Description and modes of application

Main mechanisms of the operation of a realized host system for integration of the components of a linguistic processor are considered. The system described in this paper makes it possible to use the available components of linguistic processors in a special system for automatic text processing. This host system allows also comparison of the inline components against the same sets of texts written in a natural language. After the comparative analysis of the components, the exact composition of modules and dictionaries that can be used most advantageously for developing a separate system of automatic text processing for solution of particular problems can be determined.     

Language and communication in mathematics education: an overview of research in the field

Within the field of mathematics education, the central role language plays in the learning, teaching, and doing of mathematics is increasingly recognised, but there is not agreement about what this role (or these roles) might be or even about what the term ‘language’ itself encompasses. In this issue of ZDM, we have compiled a collection of scholarship on language in mathematics education research, representing a range of approaches to the topic. In this survey paper, we outline a categorisation of ways of conceiving of language and its relevance to mathematics education, the theoretical resources drawn upon to systematise these conceptions, and the methodological approaches employed by researchers. We identify four broad areas of concern in mathematics education that are addressed by language-oriented research: analysis of the development of students’ mathematical knowledge; understanding the shaping of mathematical activity; understanding processes of teaching and learning in relation to other social interactions; and multilingual contexts. A further area of concern that has not yet received substantial attention within mathematics education research is the development of the linguistic competencies and knowledge required for participation in mathematical practices. We also discuss methodological issues raised by the dominance of English within the international research community and suggest some implications for researchers, editors and publishers.     

基于犹豫模糊语言环境的投资组合优化研究

跟传统模糊投资组合相比,基于犹豫模糊语言环境的投资组合不仅可以使用自然语言对金融资产及其不确定程度进行评价,还可以避免评价过程中信息的丢失。本文根据犹豫模糊语言投资组合综合评价系统,对不同金融产品计算得分。通过设置不同的语言尺度函数的参数值及犹豫模糊语言优化模型的临界值,针对激进型、稳健型和保守型三类投资者分别提出了收益最大化和风险最小化犹豫模糊语言投资组合模型,对建立的非线性模型进行求解,得到犹豫模糊语言投资组合的最优解。最后,用数值仿真验证了模型的合理性和有效性。     

基于实验设计的概率语言权重信息多准则决策方法

作为模糊语言集的一种,概率语言集能够反映决策问题中评价准则权重重要程度及其概率,这在决策问题中较为实用。本文运用实验设计(Design of Experiment,DOE)的方法,对权重信息以概率语言给出的多准则决策问题进行研究:通过多次模拟权重重要程度及其概率,设计出多组实验权重,并用GRA法求得每组实验数据的得分,获得描述该决策问题准则值与评价结果相互影响关系的最适用回归方程,将决策问题的实际数据带入方程进行运算,得出方案排序结果。通过快速成型过程、柔性制造系统过程两个案例,进行对比验证。结果表明所提出的方法能较好地处理基于概率语言权重信息的多准则决策问题,计算简单且速度快,可重复性强且颇为实用。     

Stretching,sliding and strategy: indexicality in algebraic explanations

In this study, we describe the linguistic expression of strategy in explanations of algebraic procedures. Stating the steps of an algebraic procedure does not require a student to indicate the relationship between different mathematical actions, but describing algebraic strategy does. The coordinated nature of strategic proficiency suggests that linguistic forms known as indexical language, “pointing words” that link speech to context, may be fundamental resources for expressing this type of competence. A class of first-year university mathematics students developed a habit of reporting procedures that we consider a speech genre. The classroom genre emphasised procedural explanations, but when students expressed strategic competence, they often relied on indexical language. Indexical verbs of motion like slide and drop proved to be a particularly efficient means of expressing algebraic strategies. This informal speech style extended the communicative capacity of the classroom speech genre, and allowed classmates to participate better in strategic mathematical reasoning.     

Linguistic modelling and information coarsening based on prototype theory and label semantics

The theory of prototypes provides a new semantic interpretation of vague concepts. In particular, the calculus derived from this interpretation results in the same calculus as label semantics proposed by Lawry. In the theory of prototypes, each basic linguistic label L has the form ‘about P’, where P is a set of prototypes of L and the neighborhood size of the underlying concept is described by the word ‘about’ which represents a probability density function δ on [0,+∞). In this paper we propose an approach to vague information coarsening based on the theory of prototypes. Moreover, we propose a framework for linguistic modelling within the theory of prototypes, in which the rules are concise and transparent. We then present a linguistic rule induction method from training data based on information coarsening and data clustering. Finally, we apply this linguistic modelling method to some benchmark time series prediction problems, which show that our linguistic modelling and information coarsening methods are potentially powerful tools for linguistic modelling and uncertain reasoning.     

Language Influence on Children's Cognitive Number Representation

This study examined the effect of language on children's cognitive representation of number. The sample for the study consisted of 90 Arabic speaking children with a mean age of 80 months. Children were interviewed individually and asked to represent written two‐digit numbers using base‐10 blocks. A new approach for testing the linguistic relativity hypothesis was used. The results of the study revealed that language played an important role in children's cognitive number representation. On the other hand, the results support the argument that the instructions given with the task alter children's performance on it. This study suggests that language may explain the cross‐cultural differences in mathematics achievement. However, the disadvantage that the language might place on children can be overcome with well‐planned instruction.     

A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts

Group decision making is a type of decision problem in which multiple experts acting collectively, analyze problems, evaluate alternatives, and select a solution from a collection of alternatives. As the natural language is the standard representation of those concepts that humans use for communication, it seems natural that they use words (linguistic terms) instead of numerical values to provide their opinions. However, while linguistic information is readily available, it is not operational and thus it has to be made usable though expressing it in terms of information granules. To do so, Granular Computing, which has emerged as a unified and coherent framework of designing, processing, and interpretation of information granules, can be used. The aim of this paper is to present an information granulation of the linguistic information used in group decision making problems defined in heterogeneous contexts, i.e., where the experts have associated importance degrees reflecting their ability to handle the problem. The granulation of the linguistic terms is formulated as an optimization problem, solved by using the particle swarm optimization, in which a performance index is maximized by a suitable mapping of the linguistic terms on information granules formalized as sets. This performance index is expressed as a weighted aggregation of the individual consistency achieved by each expert.     

Can chunking reduce syntactic complexity of natural languages?

Natural language is a complex adaptive system with multiple levels. The hierarchical structure may have much to do with the complexity of language. Dependency Distance has been invoked to explain various linguistic patterns regarding syntactic complexity. However, little attention has been paid to how the structural properties of language to minimize dependency distance. This article computationally simulates several chunked artificial languages, and shows, through comparison with Mandarin Chinese, that chunking may significantly reduce mean dependency distance of linear sequences. These results suggest that language may have evolved the mechanism of dynamic chunking to reduce the complexity for the sake of efficient communication. © 2016 Wiley Periodicals, Inc. Complexity 21: 33–41, 2016