Algebraic Structures In Natural Language
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Algebraic Structures In Natural Language
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Author : Shalom Lappin
language : en
Publisher: CRC Press
Release Date : 2022-12-23
Algebraic Structures In Natural Language written by Shalom Lappin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-23 with Computers categories.
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.
Algebraic Structures Using Natural Class Of Intervals
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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Educational Publishers & Distributors
Release Date : 2014-05-14
Algebraic Structures Using Natural Class Of Intervals written by W. B. Vasantha Kandasamy and has been published by Educational Publishers & Distributors this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
N Algebraic Structures
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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2005-01-01
N Algebraic Structures written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
In this book, for the first time we introduce the notions of N-groups, N-semigroups, N-loops and N-groupoids. We also define a mixed N-algebraic structure. The book is organized into six chapters. The first chapter gives the basic notions of S-semigroups, S-groupoids and S-loops thereby making the book self-contained. Chapter two introduces N-groups and their Smarandache analogues. In chapter three, N-loops and Smarandache N-loops are introduced and analyzed. Chapter four defines N-groupoids and S-N-groupoids. Since the N-semigroup structures are sandwiched between groups and groupoids, the study can be carried out without any difficulty. Mixed N-algebraic structures and S-mixed algebraic structures are given in chapter five. Some problems are suggested in chapter six. It is pertinent to mention that several exercises and problems (Some in the form of proof to the theorems are given in all the chapters.) A reader who attempts to solve them will certainly gain a sound knowledge about these concepts. We have given 50 problems for the reader to solve in chapter 6. The main aim of this book is to introduce new concepts and explain them with examples there by encouraging young mathematics to pursue research in this direction. Several theorems based on the definition can be easily proved with simple modification. Innovative readers can take up that job. Also these notions find their applications in automaton theory and coloring problems. The N-semigroups and N-automaton can be applied to construct finite machines, which can perform multitasks, so their capability would be much higher than the usual automaton of finite machines constructed. We have suggested a list of references for further reading.
An Introduction To Algebraic Structures
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Author : Joseph Landin
language : en
Publisher: Courier Corporation
Release Date : 2012-08-29
An Introduction To Algebraic Structures written by Joseph Landin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-29 with Mathematics categories.
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.
An Introduction To Algebraic Structures
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Author : Azriel Rosenfeld
language : en
Publisher:
Release Date : 1968
An Introduction To Algebraic Structures written by Azriel Rosenfeld and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
Algebraic Structures Using Subsets
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Author : W. B. Vasantha Kandasamy, Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2012
Algebraic Structures Using Subsets written by W. B. Vasantha Kandasamy, Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Algebra, Boolean categories.
"[The] study of algebraic structures using subsets [was] started by George Boole. After the invention of Boolean algebra, subsets are not used in building any algebraic structures. In this book we develop algebraic structures using subsets of a set or a group, or a semiring, or a ring, and get algebraic structures. Using group or semigroup, we only get subset semigroups. Using ring or semiring, we get only subset semirings. By this method, we get [an] infinite number of non-commutative semirings of finite order. We build subset semivector spaces, [and] describe and develop several interesting properties about them."--
Applied Discrete Structures Part 2 Algebraic Structures
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Author : Ken Levasseur
language : en
Publisher: Lulu.com
Release Date : 2017-05-15
Applied Discrete Structures Part 2 Algebraic Structures written by Ken Levasseur and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-15 with categories.
Applied Discrete Structures, Part II - Algebraic Structures, is an introduction to groups, monoids, vector spaces, lattices, boolean algebras, rings and fields. It corresponds with the content of Discrete Structures II at UMass Lowell, which is a required course for students in Computer Science. It presumes background contained in Part I - Fundamentals. Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.
Discrete Structures And Automata Theory
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Author : Rakesh Dube
language : en
Publisher: Alpha Science Int'l Ltd.
Release Date : 2006
Discrete Structures And Automata Theory written by Rakesh Dube and has been published by Alpha Science Int'l Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Computers categories.
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.
Logic And Algebraic Structures In Quantum Computing
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Author : Jennifer Chubb
language : en
Publisher: Cambridge University Press
Release Date : 2016-02-26
Logic And Algebraic Structures In Quantum Computing written by Jennifer Chubb and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-26 with Computers categories.
Experts in the field explore the connections across physics, quantum logic, and quantum computing.
Algebraic Systems
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Author : Anatolij Ivanovic Mal'cev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Systems written by Anatolij Ivanovic Mal'cev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.