Download or read book Algebraic Structures in Natural Language written by Shalom Lappin and published by CRC Press. This book was released on 2022-12-23 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic Structures in Natural Language written by Shalom Lappin and published by CRC Press. This book was released on 2022-12-23 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Algebraic Structures written by Joseph Landin and published by Courier Corporation. This book was released on 2012-08-29 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Logic and Algebraic Structures in Quantum Computing written by Jennifer Chubb and published by Cambridge University Press. This book was released on 2016-02-26 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebra Structure Sense Development amongst Diverse Learners written by Teresa Rojano and published by Taylor & Francis. This book was released on 2022-06-07 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Structures of Natural Intelligence written by Yair Neuman and published by Springer. This book was released on 2017-12-01 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometric and Algebraic Structures in Differential Equations written by P.H. Kersten and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics Classrooms That Promote Understanding written by Elizabeth Fennema and published by Routledge. This book was released on 1999-04-01 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book algebraic structure and matrices written by E. A. Maxwell and published by CUP Archive. This book was released on 1969 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Soft Computing in Humanities and Social Sciences written by Rudolf Seising and published by Springer. This book was released on 2011-11-22 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of Soft Computing in Humanities and Social Sciences is at a turning point. The strong distinction between “science” and “humanities” has been criticized from many fronts and, at the same time, an increasing cooperation between the so-called “hard sciences” and “soft sciences” is taking place in a wide range of scientific projects dealing with very complex and interdisciplinary topics. In the last fifteen years the area of Soft Computing has also experienced a gradual rapprochement to disciplines in the Humanities and Social Sciences, and also in the field of Medicine, Biology and even the Arts, a phenomenon that did not occur much in the previous years. The collection of this book presents a generous sampling of the new and burgeoning field of Soft Computing in Humanities and Social Sciences, bringing together a wide array of authors and subject matters from different disciplines. Some of the contributors of the book belong to the scientific and technical areas of Soft Computing while others come from various fields in the humanities and social sciences such as Philosophy, History, Sociology or Economics. Rudolf Seising received a Ph.D. degree in philosophy of science and a postdoctoral lecture qualification (PD) in history of science from the Ludwig Maximilians University of Munich. He is an Adjoint Researcher at the European Centre for Soft Computing in Mieres (Asturias), Spain. Veronica Sanz earned a Ph.D. in Philosophy at the University Complutense of Madrid (Spain). At the moment she is a Postdoctoral Researcher at the Science, Technology and Society Center in the University of California at Berkeley. Veronica Sanz earned a Ph.D. in Philosophy at the University Complutense of Madrid (Spain). At the moment she is a Postdoctoral Researcher at the Science, Technology and Society Center in the University of California at Berkeley.
Download or read book Neural Mechanisms of Language written by Maria Mody and published by Springer. This book was released on 2017-10-24 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important volume brings together significant findings on the neural bases of spoken language –its processing, use, and organization, including its phylogenetic roots. Employing a potent mix of conceptual and neuroimaging-based approaches, contributors delve deeply into specialized structures of the speech system, locating sensory and cognitive mechanisms involved in listening and comprehension, grasping meanings and storing memories. The novel perspectives revise familiar models by tracing linguistic interactions within and between neural systems, homing in on the brain’s semantic network, exploring the neuroscience behind bilingualism and multilingual fluency, and even making a compelling case for a more nuanced participation of the motor system in speech. From these advances, readers have a more three-dimensional picture of the brain—its functional epicenters, its connections, and the whole—as the seat of language in both wellness and disorders. Included in the topics: · The interaction between storage and computation in morphosyntactic processing. · The role of language in structure-dependent cognition. · Multisensory integration in speech processing: neural mechanisms of cross-modal after-effect. · A neurocognitive view of the bilingual brain. · Causal modeling: methods and their application to speech and language. · A word in the hand: the gestural origins of language. Neural Mechanisms of Language presents a sophisticated mix of detail and creative approaches to understanding brain structure and function, giving neuropsychologists, cognitive neuroscientists, developmental psychologists, cognitive psychologists, and speech/language pathologists new windows onto the research shaping their respective fields.
Download or read book Logic Methodology and Philosophy of Science VI written by J.J. Cohen and published by Elsevier. This book was released on 2011-10-10 with total page 871 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic, Methodology and Philosophy of Science VI presents the results of recent research into the foundations of science. The volume contains invited papers presented at the Congress, covering the areas of Logic, Mathematics, Physical Sciences, Biological Sciences and the Humanities.
Download or read book Natural Language Processing written by Epaminondas Kapetanios and published by CRC Press. This book was released on 2013-11-14 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the semantic aspects of natural language processing and its applications. Topics covered include: measuring word meaning similarity, multi-lingual querying, and parametric theory, named entity recognition, semantics, query language, and the nature of language. The book also emphasizes the portions of mathematics needed to under
Download or read book Theoretical Advances and Applications of Fuzzy Logic and Soft Computing written by Oscar Castillo and published by Springer Science & Business Media. This book was released on 2007-10-10 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises a selection of papers on theoretical advances and applications of fuzzy logic and soft computing from the IFSA 2007 World Congress, held in Cancun, Mexico, June 2007. These papers constitute an important contribution to the theory and applications of fuzzy logic and soft computing methodologies.
Download or read book The Oxford Handbook of Philosophy of Mathematics and Logic written by Stewart Shapiro and published by Oxford University Press. This book was released on 2005-02-10 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.
Download or read book Algebraic Systems written by Anatolij Ivanovic Mal'cev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: As far back as the 1920's, algebra had been accepted as the science studying the properties of sets on which there is defined a particular system of operations. However up until the forties the overwhelming majority of algebraists were investigating merely a few kinds of algebraic structures. These were primarily groups, rings and lattices. The first general theoretical work dealing with arbitrary sets with arbitrary operations is due to G. Birkhoff (1935). During these same years, A. Tarski published an important paper in which he formulated the basic prin ciples of a theory of sets equipped with a system of relations. Such sets are now called models. In contrast to algebra, model theory made abun dant use of the apparatus of mathematical logic. The possibility of making fruitful use of logic not only to study universal algebras but also the more classical parts of algebra such as group theory was dis covered by the author in 1936. During the next twenty-five years, it gradually became clear that the theory of universal algebras and model theory are very intimately related despite a certain difference in the nature of their problems. And it is therefore meaningful to speak of a single theory of algebraic systems dealing with sets on which there is defined a series of operations and relations (algebraic systems). The formal apparatus of the theory is the language of the so-called applied predicate calculus. Thus the theory can be considered to border on logic and algebra.
Download or read book Discrete Structures and Automata Theory written by Rakesh Dube and published by Alpha Science Int'l Ltd.. This book was released on 2006 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete Structures and Automata Theory is designed for an introductory course on formal languages, automata and discrete mathematics. Divided into two parts it covers discrete methods - stressing the finite nature in many problems and structures; combinatorics - the algebra of enumeration or coding and finite algebraic structures - effecting coding theory, method of enumeration, gating networks and combinatorial designs. It also discusses the applications of Automata Theory in Compiler design, Natural Language Processing and development of new programming languages.
