Druid Magazine

Author : René Cori
Genre : Mathematics
Publisher : Oxford University Press, USA
ISBN : 0198500513
Type book : PDF, Epub, Kindle and Mobi
File Download : 360 page
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Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. It is a major element in theoretical computer science and has undergone a huge revival with the ever-growing importance of computer science. This text is based on a course to undergraduates and provides a clear and accessible introduction to mathematical logic. The concept of model provides the underlying theme, giving the text a theoretical coherence whilst still covering a wide area of logic. The foundations having been laid in Part 1, this book starts with recursion theory, a topic essential for the complete scientist. Then follows Godel's incompleteness theorems and axiomatic set theory. Chapter 8 provides an introduction to model theory. There are examples throughout each section, and varied selection of exercises at the end. Answers to the exercises are given in the appendix.

Author : David J. Lobina
Genre : Language Arts & Disciplines
Publisher : Oxford University Press
ISBN : 9780198785156
Type book : PDF, Epub, Kindle and Mobi
File Download : 245 page
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The book examines one of the most contested topics in linguistics and cognitive science: the role of recursion in language. It offers a precise account of what recursion is, what role it should play in cognitive theories of human knowledge, and how it manifests itself in the mental representations of language and other cognitive domains.

Author : Luiz Amaral
Genre : Language Arts & Disciplines
Publisher : Cambridge University Press
ISBN : 9781108314169
Type book : PDF, Epub, Kindle and Mobi
File Download : 410 page
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Recursion and self-embedding are at the heart of our ability to formulate our thoughts, articulate our imagination and share with other human beings. Nonetheless, controversy exists over the extent to which recursion is shared across all domains of syntax. A collection of 18 studies are presented here on the central linguistic property of recursion, examining a range of constructions in over a dozen languages representing great areal, typological and genetic diversity and spanning wide latitudes. The volume expands the topic to include prepositional phrases, possessives, adjectives, and relative clauses - our many vehicles to express creative thought - to provide a critical perspective on claims about how recursion connects to broader aspects of the mind. Parallel explorations across language families, literate and non-literate societies, children and adults are investigated and constitutes a new step in the generative tradition by simultaneously focusing on formal theory, acquisition and experimentation, and ecologically-sensitive fieldwork, and initiates a new community where these diverse experts collaborate.

Author : Francis Lowenthal
Genre : Psychology
Publisher : Springer Science & Business Media
ISBN : 9781461494140
Type book : PDF, Epub, Kindle and Mobi
File Download : 232 page
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As humans, our many levels of language use distinguish us from the rest of the animal world. For many scholars, it is the recursive aspect of human speech that makes it truly human. But linguists continue to argue about what recursion actually is, leading to the central dilemma: is full recursion, as defined by mathematicians, really necessary for human language? Language and Recursion defines the elusive construct with the goal of furthering research into language and cognition. An up-to-date literature review surveys extensive findings based on non-verbal communication devices and neuroimaging techniques. Comparing human and non-human primate communication, the book’s contributors examine meaning in chimpanzee calls, and consider the possibility of a specific brain structure for recursion. The implications are then extended to formal grammars associated with artificial intelligence, and to the question of whether recursion is a valid concept at all. Among the topics covered: • The pragmatic origins of recursion. • Recursive cognition as a prelude to language. • Computer simulations of recursive exercises for a non-verbal communication device. • Early rule learning ability and language acquisition. • Computational language related to recursion, incursion, and fractals • Why there may be no recursion in language. Regardless of where one stands in the debate, Language and Recursion has much to offer the science community, particularly cognitive psychologists and researchers in the science of language. By presenting these multiple viewpoints, the book makes a solid case for eventual reconciliation.

Author : Harry van der Hulst
Genre : Language Arts & Disciplines
Publisher : Walter de Gruyter
ISBN : 9783110219258
Type book : PDF, Epub, Kindle and Mobi
File Download : 469 page
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The present volume is an edited collection of original contributions which all deal with the issue of recursion in human language(s). All contributions originate as papers that were presented at a conference on the topic of recursion in human language organized by Dan Everett in March 22, 2007. For the purpose of this collection all articles underwent a double-blind peer-review process. The present chapters were written in the course of 2008. Although the ‘recursive’ nature of linguistic expressions, i.e. the apparent possibility of producing an infinite number of expressions with finite means, has been noted for a long time, no general agreement seems to exist concerning the empirical status as well as mathematical formalization of this ‘characteristic’ of human languages or of the grammars that lie behind these utterances that make up these languages. Renewed interest in this subject was sparked by recent claims that ‘recursion’ is perhaps the sole uniquely human and as such universal trait of human language (cf. Chomsky, Hauser and Fitch 2000). In this volume, the issue of recursion is tackled from a variety of angles. Some articles cover formal issues regarding the proper characterization or definition of recursion, while others focus on empirical issues by examining the kinds of structure in languages that suggest recursive mechanism in the grammar. Most articles discuss syntactic phenomena, but several involve morphology, the lexicon and phonology. In addition, we find discussions that involve evolutionary notions and language disorders, and the broader cognitive context of recursion.

Author : Al Sweigart
Genre : Computers
Publisher : No Starch Press
ISBN : 9781718502024
Type book : PDF, Epub, Kindle and Mobi
File Download : 330 page
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An accessible yet rigorous crash course on recursive programming using Python and JavaScript examples. Recursion has an intimidating reputation: it’s considered to be an advanced computer science topic frequently brought up in coding interviews. But there’s nothing magical about recursion. The Recursive Book of Recursion uses Python and JavaScript examples to teach the basics of recursion, exposing the ways that it’s often poorly taught and clarifying the fundamental principles of all recursive algorithms. You’ll learn when to use recursive functions (and, most importantly, when not to use them), how to implement the classic recursive algorithms often brought up in job interviews, and how recursive techniques can help solve countless problems involving tree traversal, combinatorics, and other tricky topics. This project-based guide contains complete, runnable programs to help you learn: How recursive functions make use of the call stack, a critical data structure almost never discussed in lessons on recursion How the head-tail and “leap of faith” techniques can simplify writing recursive functions How to use recursion to write custom search scripts for your filesystem, draw fractal art, create mazes, and more How optimization and memoization make recursive algorithms more efficient Al Sweigart has built a career explaining programming concepts in a fun, approachable manner. If you’ve shied away from learning recursion but want to add this technique to your programming toolkit, or if you’re racing to prepare for your next job interview, this book is for you.

Author : Peter G. Hinman
Genre : Mathematics
Publisher : Cambridge University Press
ISBN : 9781107168244
Type book : PDF, Epub, Kindle and Mobi
File Download : 493 page
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The theory set out in this book results from the meeting of descriptive set theory and recursion theory.

Author : M. Fitting
Genre : Mathematics
Publisher : Elsevier
ISBN : 9780080960319
Type book : PDF, Epub, Kindle and Mobi
File Download : 328 page
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Fundamentals of Generalized Recursion Theory

Author : Raymond M. Smullyan
Genre : Social Science
Publisher : Oxford University Press on Demand
ISBN : 9780195082326
Type book : PDF, Epub, Kindle and Mobi
File Download : 180 page
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This work is a sequel to the author's G�del's Incompleteness Theorems, though it can be read independently by anyone familiar with G�del's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.

Author : Gerald E. Sacks
Genre : Mathematics
Publisher : Cambridge University Press
ISBN : 9781316739464
Type book : PDF, Epub, Kindle and Mobi
File Download : page
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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the second publication in the Perspectives in Logic series, is an almost self-contained introduction to higher recursion theory, in which the reader is only assumed to know the basics of classical recursion theory. The book is divided into four parts: hyperarithmetic sets, metarecursion, α-recursion, and E-recursion. This text is essential reading for all researchers in the field.