Computability And Logic
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Computability And Logic
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Author : George S. Boolos
language : en
Publisher: Cambridge University Press
Release Date : 2007-09-17
Computability And Logic written by George S. Boolos 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 2007-09-17 with Computers categories.
This fifth edition of 'Computability and Logic' covers not just the staple topics of an intermediate logic course such as Godel's incompleteness theorems, but also optional topics that include Turing's theory of computability and Ramsey's theorem.
Proofs And Algorithms
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Author : Gilles Dowek
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-11
Proofs And Algorithms written by Gilles Dowek 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 2011-01-11 with Computers categories.
Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation. Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself. Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.
Computability In Context Computation And Logic In The Real World
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Author : S Barry Cooper
language : en
Publisher: World Scientific
Release Date : 2011-02-25
Computability In Context Computation And Logic In The Real World written by S Barry Cooper and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-25 with Mathematics categories.
Computability has played a crucial role in mathematics and computer science, leading to the discovery, understanding and classification of decidable/undecidable problems, paving the way for the modern computer era, and affecting deeply our view of the world. Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions about the so-called Turing barrier.This volume addresses various aspects of the ways computability and theoretical computer science enable scientists and philosophers to deal with mathematical and real-world issues, covering problems related to logic, mathematics, physical processes, real computation and learning theory. At the same time it will focus on different ways in which computability emerges from the real world, and how this affects our way of thinking about everyday computational issues./a
Logic Logic And Logic
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Author : George Boolos
language : en
Publisher: Harvard University Press
Release Date : 1998
Logic Logic And Logic written by George Boolos and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.
Computability And Randomness
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Author : André Nies
language : en
Publisher: OUP Oxford
Release Date : 2009-01-29
Computability And Randomness written by André Nies and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-29 with Philosophy categories.
The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory. The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.
Discrete Structures Logic And Computability
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Author : James L. Hein
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2001
Discrete Structures Logic And Computability written by James L. Hein and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.
Discrete Structure, Logic, and Computability introduces the beginning computer science student to some of the fundamental ideas and techniques used by computer scientists today, focusing on discrete structures, logic, and computability. The emphasis is on the computational aspects, so that the reader can see how the concepts are actually used. Because of logic's fundamental importance to computer science, the topic is examined extensively in three phases that cover informal logic, the technique of inductive proof; and formal logic and its applications to computer science.
Computability Complexity Logic
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Author : E. Börger
language : en
Publisher: North Holland
Release Date : 1989-07
Computability Complexity Logic written by E. Börger and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-07 with Computers categories.
The theme of this book is formed by a pair of concepts: the concept of formal language as carrier of the precise expression of meaning, facts and problems, and the concept of algorithm or calculus, i.e. a formally operating procedure for the solution of precisely described questions and problems. The book is a unified introduction to the modern theory of these concepts, to the way in which they developed first in mathematical logic and computability theory and later in automata theory, and to the theory of formal languages and complexity theory. Apart from considering the fundamental themes and classical aspects of these areas, the subject matter has been selected to give priority throughout to the new aspects of traditional questions, results and methods which have developed from the needs or knowledge of computer science and particularly of complexity theory. It is both a textbook for introductory courses in the above-mentioned disciplines as well as a monograph in which further results of new research are systematically presented and where an attempt is made to make explicit the connections and analogies between a variety of concepts and constructions.
Fundamentals Of Logic And Computation
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Author : Zhe Hou
language : en
Publisher: Springer
Release Date : 2022-12-05
Fundamentals Of Logic And Computation written by Zhe Hou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-05 with Computers categories.
This textbook aims to help the reader develop an in-depth understanding of logical reasoning and gain knowledge of the theory of computation. The book combines theoretical teaching and practical exercises; the latter is realised in Isabelle/HOL, a modern theorem prover, and PAT, an industry-scale model checker. I also give entry-level tutorials on the two software to help the reader get started. By the end of the book, the reader should be proficient in both software. Content-wise, this book focuses on the syntax, semantics and proof theory of various logics; automata theory, formal languages, computability and complexity. The final chapter closes the gap with a discussion on the insight that links logic with computation. This book is written for a high-level undergraduate course or a Master's course. The hybrid skill set of practical theorem proving and model checking should be helpful for the future of readers should they pursue a research career or engineering in formal methods.
Martin Davis On Computability Computational Logic And Mathematical Foundations
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Author : Eugenio G. Omodeo
language : en
Publisher: Springer
Release Date : 2018-05-03
Martin Davis On Computability Computational Logic And Mathematical Foundations written by Eugenio G. Omodeo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-03 with Philosophy categories.
This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individual contributions touch on most of the core aspects of Davis’ work and set it in a contemporary context. They analyse, discuss and develop many of the ideas and concepts that Davis put forward, including such issues as contemporary satisfiability solvers, essential unification, quantum computing and generalisations of Hilbert’s tenth problem. The book starts out with a scientific autobiography by Davis, and ends with his responses to comments included in the contributions. In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’ work. As a whole, this book shows how Davis’ scientific work lies at the intersection of computability, theoretical computer science, foundations of mathematics, and philosophy, and draws its unifying vision from his deep involvement in Logic.