Language Processing Problems

Deep learning is revolutionizing how machine translation systems are built today. This book introduces the challenge of machine translation and evaluation - including historical, linguistic, and applied context -- then develops the core deep learning methods used for natural language applications. Code examples in Python give readers a hands-on blueprint for understanding and implementing their own machine translation systems. The book also provides extensive coverage of machine learning tricks, issues involved in handling various forms of data, model enhancements, and current challenges and methods for analysis and visualization. Summaries of the current research in the field make this a state-of-the-art textbook for undergraduate and graduate classes, as well as an essential reference for researchers and developers interested in other applications of neural methods in the broader field of human language processing.

Narratives enable readers to vividly experience fictional and non-fictional contexts. Writers use a variety of language features to control these experiences: they direct readers in how to construct contexts, how to draw inferences and how to identify the key parts of a story. Writers can skilfully convey physical sensations, prompt emotional states, effect moral responses and even alter the readers' attitudes. Mind, Brain and Narrative examines the psychological and neuroscientific evidence for the mechanisms which underlie narrative comprehension. The authors explore the scientific developments which demonstrate the importance of attention, counterfactuals, depth of processing, perspective and embodiment in these processes. In so doing, this timely, interdisciplinary work provides an integrated account of the research which links psychological mechanisms of language comprehension to humanities work on narrative and style.

Semantic Leaps explores how people combine knowledge from different domains in order to understand and express new ideas. Concentrating on dynamic aspects of on-line meaning construction, Coulson identifies two related sets of processes: frame-shifting and conceptual blending. Frame-shifting is semantic reanalysis in which existing elements in the contextual representation are reorganized into a new frame. Conceptual blending is a set of cognitive operations for combining partial cognitive models. By addressing linguistic phenomena often ignored in traditional meaning research, Coulson explains how processes of cross-domain mapping, frame-shifting and conceptual blending enhance the explanatory adequacy of traditional frame-based systems for natural language processing. The focus is on how the constructive processes speakers use to assemble, link and adapt simple cognitive models underlie a broad range of productive language behaviour.

Master the practical aspects of implementing deep learning solutions with PyTorch, using a hands-on approach to understanding both theory and practice. This updated edition will prepare you for applying deep learning to real world problems with a sound theoretical foundation and practical know-how with PyTorch, a platform developed by Facebook's Artificial Intelligence Research Group.You'll start with a perspective on how and why deep learning with PyTorch has emerged as an path-breaking framework with a set of tools and techniques to solve real-world problems. Next, the book will ground you with the mathematical fundamentals of linear algebra, vector calculus, probability and optimization. Having established this foundation, you'll move on to key components and functionality of PyTorch including layers, loss functions and optimization algorithms. You'll also gain an understanding of Graphical Processing Unit (GPU) based computation, which is essential for training deep learning models

In the context of this book, adaptation is taken to mean a feature of a system aimed at achieving the best possible performance, when mathematical models of the environment and the system itself are not fully available. This has applications ranging from theories of visual perception and the processing of information, to the more technical problems of friction compensation and adaptive classification of signals in fixed-weight recurrent neural networks. Largely devoted to the problems of adaptive regulation, tracking and identification, this book presents a unifying system-theoretic view on the problem of adaptation in dynamical systems. Special attention is given to systems with nonlinearly parameterized models of uncertainty. Concepts, methods and algorithms given in the text can be successfully employed in wider areas of science and technology. The detailed examples and background information make this book suitable for a wide range of researchers and graduates in cybernetics, mathe

This stimulating volume on vision extends well beyond the traditional areas of vision research and places the subject in a much broader philosophical context. The emphasis throughout is to integrate and illuminate the visual process. The first three parts of the volume provide authoritative overviews on computational vision and neural networks, on the neurophysiology of visual cortex processing, and on eye-movement research. Each of these parts illustrates how different research perspectives may jointly solve fundamental problems related to the efficiency of visual perception, to the relationship between vision and eye-movements and to the neurophysiological 'codes' underlying our visual perceptions. In the fourth part, leading vision scientists introduce the reader to some major philosophical problems in vision research such as the nature of 'ultimate' codes for perceptual events, the duality of psycho-physics, the bases of visual recognition and the paradigmatic foundations of comput

Originally published in 1966, Beryl Loftman Bailey's book was one of the first on the Jamaican Creole language, its origins and its influence on the teaching of English in Jamaica. A native Jamaican herself, Bailey's personal experience of both learning and later teaching English in the Caribbean was a springboard to her interest in the problems of language interference in contact situations. She challenged a notion prevalent throughout English teachers in Caribbean at the time that Creole was a 'dialect' not a language and therefore need not be considered in teaching. The social implications of this view are also explored. Bailey's detailed analysis of Jamaican Creole phonology, morphology, kernel sentence structure and simple and double-based transformations provided valuable insights into the foundations of the language and its educational implications.

Critical Pragmatics develops three ideas: language is a way of doing things with words; meanings of phrases and contents of utterances derive ultimately from human intentions; and language combines with other factors to allow humans to achieve communicative goals. In this book, Kepa Korta and John Perry explain why critical pragmatics provides a coherent picture of how parts of language study fit together within the broader picture of human thought and action. They focus on issues about singular reference, that is, talk about particular things, places or people, which have played a central role in the philosophy of language for more than a century. They argue that attention to the 'reflexive' or 'utterance-bound' contents of utterances sheds new light on these old problems. Their important study proposes a new approach to pragmatics and should be of wide interest to philosophers of language and linguists.

Critical Pragmatics develops three ideas: language is a way of doing things with words; meanings of phrases and contents of utterances derive ultimately from human intentions; and language combines with other factors to allow humans to achieve communicative goals. In this book, Kepa Korta and John Perry explain why critical pragmatics provides a coherent picture of how parts of language study fit together within the broader picture of human thought and action. They focus on issues about singular reference, that is, talk about particular things, places or people, which have played a central role in the philosophy of language for more than a century. They argue that attention to the 'reflexive' or 'utterance-bound' contents of utterances sheds new light on these old problems. Their important study proposes a new approach to pragmatics and should be of wide interest to philosophers of language and linguists.

Understanding how the Chinese writing system illustrates universal design features of writing and literacy learning, as well as how it differs from alphabetic literacy, has become one of the cutting edge areas of research in the cognitive sciences. A major part of this book is devoted to the presentation of a series of proposals for collaborative research with investigators working in East Asia on cross-writing system comparisons and bilingual literacy—Comparing alphabetic and morpho-syllabic literacy. The part that corresponds to "International perspectives" proposes new avenues in research on problems of bilingualism shared by speakers of all languages. With a broad survey of research advances drawing from recent investigations, this book will provide non-specialist readers with examples of how the relevant concepts might be applied to practical problems-age of acquisition effects in first and second language development; analysis of language attrition and asymmetries of different k

This book will strengthen a student's grasp of the laws of physics by applying them to practical situations, and problems that yield more easily to intuitive insight than brute-force methods and complex mathematics. These intriguing problems, chosen almost exclusively from classical (non-quantum) physics, are posed in accessible non-technical language requiring the student to select the right framework in which to analyse the situation and decide which branches of physics are involved. The level of sophistication needed to tackle most of the two hundred problems is that of the exceptional school student, the good undergraduate, or competent graduate student. The book will be valuable to undergraduates preparing for 'general physics' papers. It is hoped that even some physics professors will find the more difficult questions challenging. By contrast, mathematical demands are minimal, and do not go beyond elementary calculus. This intriguing book of physics problems should prove instruct

ESL/EFL Cases: Contexts for Teacher Professional Discussions is designed to provoke conversations on language teaching from multiple perspectives. The format of the presentation of cases allows the reader to gain insights on teaching from the vantage point of the students’ proficiency, the teacher’s perspective, the writers’ questions and suggested answers and finally the critical commentary. Readers are treated as thinking professionals who are capable of analysing the acts of language teaching through the teaching excerpts and the dynamic lesson transcriptions. The questions and critical commentary encourage deeper and more critical processing rather than a superficial interpretation of the teaching act. The cases, derived from authentic teaching contexts, encourage readers to appreciate the rich tapestry of teaching with all its complexities. Designed to promote professional discussions and deeper reflective and more effective practice, this book is a must for the teacher education

The field of matter transport is central to understanding the processing of materials and their subsequent mechanical properties. While thermodynamics determines the final state of a material system, it is the kinetics of mass transport that governs how it gets there. This book, first published in 2000, gives a solid grounding in the principles of matter transport and their application to a range of engineering problems. The author develops a unified treatment of mass transport applicable to both solids and liquids. Traditionally matter transport in fluids is considered as an extension of heat transfer and can appear to have little relationship to diffusion in solids. This unified approach clearly makes the connection between these important fields. This book is aimed at advanced undergraduate and beginning graduate students of materials science and engineering and related disciplines. It contains numerous worked examples and unsolved problems. The material can be covered in a one seme

The field of matter transport is central to understanding the processing of materials and their subsequent mechanical properties. While thermodynamics determines the final state of a material system, it is the kinetics of mass transport that governs how it gets there. This book, first published in 2000, gives a solid grounding in the principles of matter transport and their application to a range of engineering problems. The author develops a unified treatment of mass transport applicable to both solids and liquids. Traditionally matter transport in fluids is considered as an extension of heat transfer and can appear to have little relationship to diffusion in solids. This unified approach clearly makes the connection between these important fields. This book is aimed at advanced undergraduate and beginning graduate students of materials science and engineering and related disciplines. It contains numerous worked examples and unsolved problems. The material can be covered in a one seme

A peculiar and fascinating aspect of many responses to mass atrocities is the creative and eclectic use of religious language and frameworks. Some crimes are so extreme that they 'cry out to heaven', drawing people to employ religious vocabulary to make meaning of and to judge what happened, to deal with questions of guilt and responsibility, and to re-establish hope and trust in their lives. Moreover, in recent years, religious actors have become increasingly influential in worldwide contexts of conflict-resolution and transitional justice. This collection offers a critical assessment of the possibilities and problems pertaining to attempts to bring religious - or semi-religious - allegiances and perspectives to bear in responses to the mass atrocities of our time: When and how can religious language or religious beliefs and practices be either necessary or helpful? And what are the problems and reasons for caution or critique? In this book, a group of distinguished scholars explore t

A peculiar and fascinating aspect of many responses to mass atrocities is the creative and eclectic use of religious language and frameworks. Some crimes are so extreme that they 'cry out to heaven', drawing people to employ religious vocabulary to make meaning of and to judge what happened, to deal with questions of guilt and responsibility, and to re-establish hope and trust in their lives. Moreover, in recent years, religious actors have become increasingly influential in worldwide contexts of conflict-resolution and transitional justice. This collection offers a critical assessment of the possibilities and problems pertaining to attempts to bring religious - or semi-religious - allegiances and perspectives to bear in responses to the mass atrocities of our time: When and how can religious language or religious beliefs and practices be either necessary or helpful? And what are the problems and reasons for caution or critique? In this book, a group of distinguished scholars explore t

Now in paperback, this remains one of the classic expositions of the theory of wavelets from two of the subject's leading experts. In this volume the theory of paradifferential operators and the Cauchy kernel on Lipschitz curves are discussed with the emphasis firmly on their connection with wavelet bases. Sparse matrix representations of these operators can be given in terms of wavelet bases which have important applications in image processing and numerical analysis. This method is now widely studied and can be used to tackle a wide variety of problems arising in science and engineering. Put simply, this is an essential purchase for anyone researching the theory of wavelets.

Now in paperback, this remains one of the classic expositions of the theory of wavelets from two of the subject's leading experts. In this volume the theory of paradifferential operators and the Cauchy kernel on Lipschitz curves are discussed with the emphasis firmly on their connection with wavelet bases. Sparse matrix representations of these operators can be given in terms of wavelet bases which have important applications in image processing and numerical analysis. This method is now widely studied and can be used to tackle a wide variety of problems arising in science and engineering. Put simply, this is an essential purchase for anyone researching the theory of wavelets.

本書序言1. Vectors are introduced earlier in the text (Chapter 2) so that students develop familiarity with vector language before encountering motion in one and two dimensions.2. Updates to the text reflect current technological advances, including recent spacecraft and updated coverage of climate change.3. New STEP (Scaffolding the Essentials of Physics) problems in WebAssign offer self-paced activities that bridge the gap between basic physics knowledge and solving complex textbook problems.4. Updated Master Its in WebAssign provide just-in-time problem-solving support to students, walking through the reasoning of problems that are similar to those that appear in the text.本書特色1. A Storyline feature that begins each chapter offers a continuous story through the eyes of an inquisitive physics student, connecting topics across the textbook and relating physics to everyday life.2. The Analysis Model approach to problem solving helps students conceptualize physics problems. Introduced in Cha

This tract gives a simple but rigorous treatment of some of the mathematical problems that arise in the theory of the transfer of radiation through the atmosphere of a star. Similar problems occur in the theory of the diffusion of neutrons and in the study of temperature-wave flow in solids; so the solutions found in one theory can often be applied in the others. Dr Busbridge's starting-point is the equation of transfer. The first section provides the auxiliary mathematics, and the second discusses the Milne equations. Some unsolved and incompletely solved problems are considered in an appendix. The language and notation of astrophysics is used throughout, for brevity and simplicity, but translation into other notations is usually fairly easy. Over the years the subject had grown considerably, and several outstanding problems have been solved, though the total amount of rigorous work is small. This tract will help to clear up confusions which exist and will provide an introduction to s

Creating an orthography is often seen as a key component of language revitalisation. Encoding an endangered variety can enhance its status and prestige. In speech communities that are fragmented dialectally or geographically, a common writing system may help create a sense of unified identity, or help keep a language alive by facilitating teaching and learning. Despite clear advantages, creating an orthography for an endangered language can also bring challenges, and this volume debates the following critical questions: whose task should this be - that of the linguist or the speech community? Should an orthography be maximally distanciated from that of the language of wider communication for ideological reasons, or should its main principles coincide for reasons of learnability? Which local variety should be selected as the basis of a common script? Is a multilectal script preferable to a standardised orthography? And can creating an orthography create problems for existing native spea

At a time when many of the world's languages are at risk of extinction, the imperative to document, analyse and teach them before time runs out is very great. At this critical time new technologies, such as visual and aural archiving, digitisation of textual resources, electronic mapping and social media, have the potential to play an integral role in language maintenance and revitalisation. Drawing on studies of endangered languages from around the world - Europe, Asia, Africa and North and South America - this volume considers how these new resources might best be applied, and the problems that they can bring. It also re-assesses more traditional techniques of documentation in light of new technologies and works towards achieving a practicable synthesis of old and new methodologies. This accessible volume will be of interest to researchers in language endangerment, language typology and linguistic anthropology, and to community members working in native language maintenance.

Creating an orthography is often seen as a key component of language revitalisation. Encoding an endangered variety can enhance its status and prestige. In speech communities that are fragmented dialectally or geographically, a common writing system may help create a sense of unified identity, or help keep a language alive by facilitating teaching and learning. Despite clear advantages, creating an orthography for an endangered language can also bring challenges, and this volume debates the following critical questions: whose task should this be - that of the linguist or the speech community? Should an orthography be maximally distanciated from that of the language of wider communication for ideological reasons, or should its main principles coincide for reasons of learnability? Which local variety should be selected as the basis of a common script? Is a multilectal script preferable to a standardised orthography? And can creating an orthography create problems for existing native spea

At a time when many of the world's languages are at risk of extinction, the imperative to document, analyse and teach them before time runs out is very great. At this critical time new technologies, such as visual and aural archiving, digitisation of textual resources, electronic mapping and social media, have the potential to play an integral role in language maintenance and revitalisation. Drawing on studies of endangered languages from around the world - Europe, Asia, Africa and North and South America - this volume considers how these new resources might best be applied, and the problems that they can bring. It also re-assesses more traditional techniques of documentation in light of new technologies and works towards achieving a practicable synthesis of old and new methodologies. This accessible volume will be of interest to researchers in language endangerment, language typology and linguistic anthropology, and to community members working in native language maintenance.

Fluent aphasia is a language disorder that follows brain damage, causing difficulty in finding the correct words and structuring sentences. Speakers also experience problems in understanding language, severely impairing their ability to communicate. In this informative study Susan Edwards provides a detailed description of fluent aphasia, by drawing widely on research data, and by comparing fluent aphasia with other types of aphasia as well as with normal language. She discusses evidence that the condition affects access to underlying grammatical rules as well as to the lexicon, and explores the relationship between language and the brain, the controversy over aphasia syndromes, the assessment of aphasia via standardized tests, and the analysis of continuous speech data. Extensive examples of aphasic speech are given, and the progress of one fluent aphasic speaker is discussed in detail. Written by an internationally renowned expert, this book will be invaluable to linguists and practi

Language - in its communicative and playful functions, its literary formations and its shifting meanings - is a perennially fascinating topic. C. S. Lewis's Studies in Words explores this fascination by taking a series of words and teasing out their connotations using examples from a vast range of English literature, recovering lost meanings and analysing their functions. It doubles as an absorbing and entertaining study of verbal communication, its pleasures and problems. The issues revealed are essential to all who read and communicate thoughtfully, and are handled here by a masterful exponent and analyst of the English language.

A new, thought-provoking book on the theory of grammar and language processing, based on the analysis of authentic speech produced in real time. Drawing on insights from cognitive psychology, neurology and conversation analysis, the author offers a fascinating, easy-to-follow account of why spoken English is structured the way it is. The traditional product-based approach to grammar is given up in favour of a speaker-based, dynamic perspective that integrates language-structural, neurocognitive and dialogic aspects of speech production. Based on fresh empirical research Haselow argues that grammatical knowledge rests upon two cognitive principles of linearization called 'microgrammar' and 'macrogrammar', which are shown to interact in various ways. The book discusses a broad range of speech phenomena under an integrated framework, such as the omnipresence of 'unintegrated' constituents (e.g. discourse markers), ellipses, or the allegedly 'fragmented' character of syntax, and explains t

Bilingual language behaviour is driven by numerous factors that are usually studied in isolation, even though individual factors never operate alone. Bringing together key insights from psycholinguistics and sociolinguistics, Luna Filipović presents a new model of bilingual language processing that captures bilingualism within and across minds. The model enables readers to explain traditional puzzles in the field, and accounts for some apparently contradictory reports in different studies. It shows how theory can be applied in practice and how practice feeds back into theory, with mutual benefits. Bilinguals are studied in action, when they interact with other bilinguals or monolinguals, when they recall witnessed events in real life and in the lab and when they translate and interpret for the benefit of monolinguals. This interdisciplinary take on bilingualism in action will lead to new research on bilingualism itself, and to applications in forensic linguistics and translation studie

Bilingual language behaviour is driven by numerous factors that are usually studied in isolation, even though individual factors never operate alone. Bringing together key insights from psycholinguistics and sociolinguistics, Luna Filipović presents a new model of bilingual language processing that captures bilingualism within and across minds. The model enables readers to explain traditional puzzles in the field, and accounts for some apparently contradictory reports in different studies. It shows how theory can be applied in practice and how practice feeds back into theory, with mutual benefits. Bilinguals are studied in action, when they interact with other bilinguals or monolinguals, when they recall witnessed events in real life and in the lab and when they translate and interpret for the benefit of monolinguals. This interdisciplinary take on bilingualism in action will lead to new research on bilingualism itself, and to applications in forensic linguistics and translation studie

A new, thought-provoking book on the theory of grammar and language processing, based on the analysis of authentic speech produced in real time. Drawing on insights from cognitive psychology, neurology and conversation analysis, the author offers a fascinating, easy-to-follow account of why spoken English is structured the way it is. The traditional product-based approach to grammar is given up in favour of a speaker-based, dynamic perspective that integrates language-structural, neurocognitive and dialogic aspects of speech production. Based on fresh empirical research Haselow argues that grammatical knowledge rests upon two cognitive principles of linearization called 'microgrammar' and 'macrogrammar', which are shown to interact in various ways. The book discusses a broad range of speech phenomena under an integrated framework, such as the omnipresence of 'unintegrated' constituents (e.g. discourse markers), ellipses, or the allegedly 'fragmented' character of syntax, and explains t

Fortran is one of the oldest high-level languages and remains the premier language for writing code for science and engineering applications. This book is for anyone who uses Fortran, from the novice learner to the advanced expert. It describes best practices for programmers, scientists, engineers, computer scientists and researchers who want to apply good style and incorporate rigorous usage in their own Fortran code or to establish guidelines for a team project. The presentation concentrates primarily on the characteristics of Fortran 2003, while also describing methods in Fortran 90/95 and valuable new features in Fortran 2008. The authors draw on more than a half century of experience writing production Fortran code to present clear succinct guidelines on formatting, naming, documenting, programming and packaging conventions and various programming paradigms such as parallel processing (including OpenMP, MPI and coarrays), OOP, generic programming and C language interoperability.

Fortran is one of the oldest high-level languages and remains the premier language for writing code for science and engineering applications. This book is for anyone who uses Fortran, from the novice learner to the advanced expert. It describes best practices for programmers, scientists, engineers, computer scientists and researchers who want to apply good style and incorporate rigorous usage in their own Fortran code or to establish guidelines for a team project. The presentation concentrates primarily on the characteristics of Fortran 2003, while also describing methods in Fortran 90/95 and valuable new features in Fortran 2008. The authors draw on more than a half century of experience writing production Fortran code to present clear succinct guidelines on formatting, naming, documenting, programming and packaging conventions and various programming paradigms such as parallel processing (including OpenMP, MPI and coarrays), OOP, generic programming and C language interoperability.

●Focuses on real-world application by guiding students through practice problems and using the technique in a project●Presents a contemporary, object-oriented approach using UML (Unified Modeling Language)●Integrates stories, feedback, and advice from a diverse industry advisory board of IS professionals and consultants●Provides chapters that each cover a different step in the Systems Development Life Cycle (SDLC) process

A central theme of this book is that the main problems of philosophy and certainly the main traditional problems in the theory of knowledge, concern the space between language and the world. Professor Danto distinguishes between descriptive concepts, concerned with saying how the world is and semantic concepts, which have to do with the application of descriptions of the world. Failure to make these distinctions is responsible for a class of seemingly irresolvable disputes over the foundations of knowledge; but when the distinction is appreciated, a plausible philosophical theory of what it is to know the world can be framed which is free from the standard scepticisms.

This challenging study places fiction squarely at the centre of the discussion of metaphysics. Philosophers have traditionally treated fiction as involving a set of narrow problems in logic or the philosophy of language. By contrast Amie Thomasson argues that fiction has far-reaching implications for central problems of metaphysics. The book develops an 'artifactual' theory of fiction, whereby fictional characters are abstract artifacts as ordinary as laws or symphonies or works of literature. By understanding fictional characters we come to understand how other cultural and social objects are established on the basis of the independent physical world and the mental states of human beings.

This challenging study places fiction squarely at the centre of the discussion of metaphysics. Philosophers have traditionally treated fiction as involving a set of narrow problems in logic or the philosophy of language. By contrast Amie Thomasson argues that fiction has far-reaching implications for central problems of metaphysics. The book develops an 'artifactual' theory of fiction, whereby fictional characters are abstract artifacts as ordinary as laws or symphonies or works of literature. By understanding fictional characters we come to understand how other cultural and social objects are established on the basis of the independent physical world and the mental states of human beings.

Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decid

Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.

Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.

The authors in this 2000 collection use Vygotsky's cultural-historical theory of human development to frame their analyses of schooling, with particular emphasis on the ways in which literacy practices are mediated by social interaction and cultural artifacts. This volume extends Vygotsky's cultural-historical theoretical framework to embrace nuances of learning and development that are influenced by culture as instantiated through the experiences of race, ethnicity, and language variation. Rather than seeking to provide definitive answers to social questions using Vygotsky's core principles, the authors wrestle with educational problems through the mediation of Vygotsky's theory. In doing so, they both sharpen their focus on the problems and speak back to Vygotsky, helping to extend the foundation of his work to address modern problems. This collection serves as a form of collaborative inquiry that itself will stimulate further consideration of these topics.