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Author: Shalom Lappin
Publisher: CRC Press
ISBN: 1000817873
Category : Computers
Languages : en
Pages : 309
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Book Description
Algebraic Structures in Natural Language addresses a central problem in cognitive science concerning the learning procedures through which humans acquire and represent natural language. Until recently algebraic systems have dominated the study of natural language in formal and computational linguistics, AI, and the psychology of language, with linguistic knowledge seen as encoded in formal grammars, model theories, proof theories and other rule-driven devices. Recent work on deep learning has produced an increasingly powerful set of general learning mechanisms which do not apply rule-based algebraic models of representation. The success of deep learning in NLP has led some researchers to question the role of algebraic models in the study of human language acquisition and linguistic representation. Psychologists and cognitive scientists have also been exploring explanations of language evolution and language acquisition that rely on probabilistic methods, social interaction and information theory, rather than on formal models of grammar induction. This book addresses the learning procedures through which humans acquire natural language, and the way in which they represent its properties. It brings together leading researchers from computational linguistics, psychology, behavioral science and mathematical linguistics to consider the significance of non-algebraic methods for the study of natural language. The text represents a wide spectrum of views, from the claim that algebraic systems are largely irrelevant to the contrary position that non-algebraic learning methods are engineering devices for efficiently identifying the patterns that underlying grammars and semantic models generate for natural language input. There are interesting and important perspectives that fall at intermediate points between these opposing approaches, and they may combine elements of both. It will appeal to researchers and advanced students in each of these fields, as well as to anyone who wants to learn more about the relationship between computational models and natural language.
Author: Shalom Lappin
Publisher: CRC Press
ISBN: 1000817873
Category : Computers
Languages : en
Pages : 309
Get Book Here
Book Description
Algebraic Structures in Natural Language addresses a central problem in cognitive science concerning the learning procedures through which humans acquire and represent natural language. Until recently algebraic systems have dominated the study of natural language in formal and computational linguistics, AI, and the psychology of language, with linguistic knowledge seen as encoded in formal grammars, model theories, proof theories and other rule-driven devices. Recent work on deep learning has produced an increasingly powerful set of general learning mechanisms which do not apply rule-based algebraic models of representation. The success of deep learning in NLP has led some researchers to question the role of algebraic models in the study of human language acquisition and linguistic representation. Psychologists and cognitive scientists have also been exploring explanations of language evolution and language acquisition that rely on probabilistic methods, social interaction and information theory, rather than on formal models of grammar induction. This book addresses the learning procedures through which humans acquire natural language, and the way in which they represent its properties. It brings together leading researchers from computational linguistics, psychology, behavioral science and mathematical linguistics to consider the significance of non-algebraic methods for the study of natural language. The text represents a wide spectrum of views, from the claim that algebraic systems are largely irrelevant to the contrary position that non-algebraic learning methods are engineering devices for efficiently identifying the patterns that underlying grammars and semantic models generate for natural language input. There are interesting and important perspectives that fall at intermediate points between these opposing approaches, and they may combine elements of both. It will appeal to researchers and advanced students in each of these fields, as well as to anyone who wants to learn more about the relationship between computational models and natural language.
Author: Shalom Lappin
Publisher: CRC Press
ISBN: 1000817881
Category : Computers
Languages : en
Pages : 346
Get Book Here
Book Description
Algebraic Structures in Natural Language addresses a central problem in cognitive science concerning the learning procedures through which humans acquire and represent natural language. Until recently algebraic systems have dominated the study of natural language in formal and computational linguistics, AI, and the psychology of language, with linguistic knowledge seen as encoded in formal grammars, model theories, proof theories and other rule-driven devices. Recent work on deep learning has produced an increasingly powerful set of general learning mechanisms which do not apply rule-based algebraic models of representation. The success of deep learning in NLP has led some researchers to question the role of algebraic models in the study of human language acquisition and linguistic representation. Psychologists and cognitive scientists have also been exploring explanations of language evolution and language acquisition that rely on probabilistic methods, social interaction and information theory, rather than on formal models of grammar induction. This book addresses the learning procedures through which humans acquire natural language, and the way in which they represent its properties. It brings together leading researchers from computational linguistics, psychology, behavioral science and mathematical linguistics to consider the significance of non-algebraic methods for the study of natural language. The text represents a wide spectrum of views, from the claim that algebraic systems are largely irrelevant to the contrary position that non-algebraic learning methods are engineering devices for efficiently identifying the patterns that underlying grammars and semantic models generate for natural language input. There are interesting and important perspectives that fall at intermediate points between these opposing approaches, and they may combine elements of both. It will appeal to researchers and advanced students in each of these fields, as well as to anyone who wants to learn more about the relationship between computational models and natural language.
Author: Joseph Landin
Publisher: Courier Corporation
ISBN: 0486150410
Category : Mathematics
Languages : en
Pages : 275
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Book Description
This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.
Author: Jennifer Chubb
Publisher: Cambridge University Press
ISBN: 1316654060
Category : Mathematics
Languages : en
Pages : 355
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Book Description
Arising from a special session held at the 2010 North American Annual Meeting of the Association for Symbolic Logic, this volume is an international cross-disciplinary collaboration with contributions from leading experts exploring connections across their respective fields. Themes range from philosophical examination of the foundations of physics and quantum logic, to exploitations of the methods and structures of operator theory, category theory, and knot theory in an effort to gain insight into the fundamental questions in quantum theory and logic. The book will appeal to researchers and students working in related fields, including logicians, mathematicians, computer scientists, and physicists. A brief introduction provides essential background on quantum mechanics and category theory, which, together with a thematic selection of articles, may also serve as the basic material for a graduate course or seminar.
Author: Sergei Silvestrov
Publisher: Springer Nature
ISBN: 3030418502
Category : Mathematics
Languages : en
Pages : 976
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Book Description
This book explores the latest advances in algebraic structures and applications, and focuses on mathematical concepts, methods, structures, problems, algorithms and computational methods important in the natural sciences, engineering and modern technologies. In particular, it features mathematical methods and models of non-commutative and non-associative algebras, hom-algebra structures, generalizations of differential calculus, quantum deformations of algebras, Lie algebras and their generalizations, semi-groups and groups, constructive algebra, matrix analysis and its interplay with topology, knot theory, dynamical systems, functional analysis, stochastic processes, perturbation analysis of Markov chains, and applications in network analysis, financial mathematics and engineering mathematics. The book addresses both theory and applications, which are illustrated with a wealth of ideas, proofs and examples to help readers understand the material and develop new mathematical methods and concepts of their own. The high-quality chapters share a wealth of new methods and results, review cutting-edge research and discuss open problems and directions for future research. Taken together, they offer a source of inspiration for a broad range of researchers and research students whose work involves algebraic structures and their applications, probability theory and mathematical statistics, applied mathematics, engineering mathematics and related areas.
Author: Teresa Rojano
Publisher: Taylor & Francis
ISBN: 1000591530
Category : Education
Languages : en
Pages : 210
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Book Description
This volume emphasizes the role of effective curriculum design, teaching materials, and pedagogy to foster algebra structure sense at different educational levels. Positing algebra structure sense as fundamental to developing students’ broader mathematical maturity and advanced thinking, this text reviews conceptual, historical, cognitive, and semiotic factors, which influence the acquisition of algebra structure sense. It provides empirical evidence to demonstrate the feasibility of linking algebra structure sense to technological tools and promoting it amongst diverse learners. Didactic approaches include the use of adaptive digital environments, gamification, diagnostic and monitoring tools, as well as exercises and algebraic sequences of varied complexity. Advocating for a focus on both intuitive and formal knowledge, this volume will be of interest to students, scholars, and researchers with an interest in educational research, as well as mathematics education and numeracy.
Author: Yair Neuman
Publisher: Springer
ISBN: 3319682466
Category : Mathematics
Languages : en
Pages : 179
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Book Description
This book uncovers mathematical structures underlying natural intelligence and applies category theory as a modeling language for understanding human cognition, giving readers new insights into the nature of human thought. In this context, the book explores various topics and questions, such as the human representation of the number system, why our counting ability is different from that which is evident among non-human organisms, and why the idea of zero is so difficult to grasp. The book is organized into three parts: the first introduces the general reason for studying general structures underlying the human mind; the second part introduces category theory as a modeling language and use it for exposing the deep and fascinating structures underlying human cognition; and the third applies the general principles and ideas of the first two parts to reaching a better understanding of challenging aspects of the human mind such as our understanding of the number system, the metaphorical nature of our thinking and the logic of our unconscious dynamics.
Author: Gheorghe Paun
Publisher: World Scientific
ISBN: 9814518158
Category : Computers
Languages : en
Pages : 502
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Book Description
This book contains original reviews by well-known workers in the field of mathematical linguistics and formal language theory, written in honour of Professor Solomon Marcus on the occasion of his 70th birthday.Some of the papers deal with contextual grammars, a class of generative devices introduced by Marcus, motivated by descriptive linguistics. Others are devoted to grammar systems, a very modern branch of formal language theory. Automata theory and the algebraic approach to computer science are other well-represented areas. While the contributions are mathematically oriented, practical issues such as cryptography, grammatical inference and natural language processing are also discussed.
Author: P.H. Kersten
Publisher: Springer Science & Business Media
ISBN: 9400901798
Category : Mathematics
Languages : en
Pages : 346
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Book Description
The geometrical theory of nonlinear differential equations originates from classical works by S. Lie and A. Bäcklund. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became clear that some basic and quite general geometrical and algebraic structures govern this property of integrability. Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics. In 1993, a workshop on algebra and geometry of differential equations took place at the University of Twente (The Netherlands), where the state-of-the-art of the main problems was fixed. This book contains a collection of invited lectures presented at this workshop. The material presented is of interest to those who work in pure and applied mathematics and especially in mathematical physics.
Author: Elizabeth Fennema
Publisher: Routledge
ISBN: 113567650X
Category : Education
Languages : en
Pages : 217
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Book Description
Mathematics Classrooms That Promote Understanding synthesizes the implications of research done by the National Center for Research in Mathematical Sciences on integrating two somewhat diverse bodies of scholarly inquiry: the study of teaching and the study of learning mathematics. This research was organized around content domains and/or continuing issues of education, such as equity and assessment of learning, and was guided by two common goals--defining the mathematics content of the K-12 curriculum in light of the changing mathematical needs of citizens for the 21st century, and identifying common components of classrooms that enable students to learn the redefined mathematics with understanding. To accomplish these goals, classrooms in which instruction facilitated the growth of understanding were established and/or studied. This volume reports and discusses the findings which grew out of this research, and subsequent papers and discussions among the scholars engaged in the endeavor. Section I, "Setting the Stage," focuses on three major threads: What mathematics should be taught; how we should define and increase students' understanding of that mathematics; and how learning with understanding can be facilitated for all students. Section II, "Classrooms That Promote Understanding," includes vignettes from diverse classrooms that illustrate classroom discourse, student work, and student engagement in the mathematics described in Chapter 1 as well as the mental activities described in Chapter 2. These chapters also illustrate how teachers deal with the equity concerns described in Chapter 3. Section III addresses "Developing Classrooms That Promote Understanding." The knowledge of the teaching/learning process gained from the research reported in this volume is a necessary prerequisite for implementing the revisions called for in the current reform movement. The classrooms described show that innovative reform in teaching and learning mathematics is possible. Unlike many volumes reporting research, this book is written at a level appropriate for master's degree students. Very few references are included in the chapters themselves; instead, each chapter includes a short annotated list of articles for expanded reading which provides the scholarly basis and research substantiation for this volume.
