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Proof In Alonzo Churchs And Alan Turings Mathematical Logic Undecidability Of First Order Logic
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Book Synopsis Proof in Alonzo Church's and Alan Turing's Mathematical Logic: Undecidability of First Order Logic by :
Download or read book Proof in Alonzo Church's and Alan Turing's Mathematical Logic: Undecidability of First Order Logic written by and published by Universal-Publishers. This book was released on with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Mathematical Logic by : Elliott Mendelson
Download or read book Introduction to Mathematical Logic written by Elliott Mendelson and published by CRC Press. This book was released on 2015-05-21 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Godel, Church, Kleene, Rosse
Download or read book Logic and Metalogic written by and published by PediaPress. This book was released on with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Alan Turing's Systems of Logic by : Andrew W. Appel
Download or read book Alan Turing's Systems of Logic written by Andrew W. Appel and published by Princeton University Press. This book was released on 2021-10-12 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: A facsimile edition of Alan Turing's influential Princeton thesis Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912–1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world—including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene—were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal—a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science.
Book Synopsis The Collected Works of Alonzo Church by : Tyler Burge
Download or read book The Collected Works of Alonzo Church written by Tyler Burge and published by MIT Press. This book was released on 2019-04-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Writings, including articles, letters, and unpublished work, by one of the twentieth century's most influential figures in mathematical logic and philosophy. Alonzo Church's long and distinguished career in mathematics and philosophy can be traced through his influential and wide-ranging writings. Church published his first article as an undergraduate at Princeton in 1924 and his last shortly before his death in 1995. This volume collects all of his published articles, many of his reviews, his monograph The Calculi of Lambda-Conversion, the introduction to his important and authoritative textbook Introduction to Mathematical Logic, a substantial amount of previously unpublished work (including chapters for the unfinished second volume of Introduction to Mathematical Logic), and a selection of letters to such correspondents as Rudolf Carnap and W. V. O. Quine. With the exception of the reviews, letters, and unpublished work, these appear in chronological order, for the most part in the format in which they were originally published. Church's work in calculability, especially the monograph on the lambda-calculus, helped lay the foundation for theoretical computer science; it attracted the interest of Alan Turing, who later completed his PhD under Church's supervision. (Church coined the term “Turing machine” in a review.) Church's influential textbook, still in print, defined the field of mathematical logic for a generation of logicians. In addition, his close connection with the Association for Symbolic Logic and his many years as review editor for the Journal of Symbolic Logic are documented in the reviews included here.
Book Synopsis Introduction To Mathematical Logic (Extended Edition) by : Michal Walicki
Download or read book Introduction To Mathematical Logic (Extended Edition) written by Michal Walicki and published by World Scientific Publishing Company. This book was released on 2016-08-12 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book presupposes only elementary background and can be used also for self-study by more ambitious students.Starting with the basics of set theory, induction and computability, it covers propositional and first order logic — their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts.Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules — of a high, though often neglected, pedagogical value — aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers.An overview of the history of logic precedes the main text, while informal analogies precede introduction of most central concepts. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of logic.This revised edition contains also, besides many new exercises, a new chapter on semantic paradoxes. An equivalence of logical and graphical representations allows us to see vicious circularity as the odd cycles in the graphical representation and can be used as a simple tool for diagnosing paradoxes in natural discourse.
Book Synopsis Logic Design by : Jaden Mclean & Carmen Hurley
Download or read book Logic Design written by Jaden Mclean & Carmen Hurley and published by Scientific e-Resources. This book was released on 2019-11-07 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book attempts to achieve a balance between theory and application. For this reason, the book does not over-emphasize the mathematics of switching theory; however it does present the theory which is necessary for understanding the fundamental concepts of logic design. Written in a student-friendly style, the book provides an in-depth knowledge of logic design. Striking a balance between theory and practice, it covers topics ranging from number systems, binary codes, logic gates and Boolean algebra, design of combinational logic circuits, synchronous and asynchronous sequential circuits, etc. The main emphasis of this book is to highlight the theoretical concepts and systematic synthesis techniques that can be applied to the design of practical digital systems. This comprehensive book is written for the graduate students of electronics and communication engineering, electrical and electronics engineering, instrumentation engineering, telecommunication engineering, computer science and engineering, and information technology.
Book Synopsis In the Light of Logic by : Solomon Feferman
Download or read book In the Light of Logic written by Solomon Feferman and published by Oxford University Press. This book was released on 1998-11-19 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they engendered. He argues that the freedom provided by Cantorian set theory was purchased at a heavy philosophical price, namely adherence to a form of mathematical platonism that is difficult to support. Beginning with a previously unpublished lecture for a general audience, Deciding the Undecidable, Feferman examines the famous list of twenty-three mathematical problems posed by David Hilbert, concentrating on three problems that have most to do with logic. Other chapters are devoted to the work and thought of Kurt Gödel, whose stunning results in the 1930s on the incompleteness of formal systems and the consistency of Cantors continuum hypothesis have been of utmost importance to all subsequent work in logic. Though Gödel has been identified as the leading defender of set-theoretical platonism, surprisingly even he at one point regarded it as unacceptable. In his concluding chapters, Feferman uses tools from the special part of logic called proof theory to explain how the vast part--if not all--of scientifically applicable mathematics can be justified on the basis of purely arithmetical principles. At least to that extent, the question raised in two of the essays of the volume, Is Cantor Necessary?, is answered with a resounding no. This volume of important and influential work by one of the leading figures in logic and the foundations of mathematics is essential reading for anyone interested in these subjects.
Book Synopsis Logic as a Tool by : Valentin Goranko
Download or read book Logic as a Tool written by Valentin Goranko and published by John Wiley & Sons. This book was released on 2016-10-17 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a clear, precise and user-friendly style, Logic as a Tool: A Guide to Formal Logical Reasoning is intended for undergraduates in both mathematics and computer science, and will guide them to learn, understand and master the use of classical logic as a tool for doing correct reasoning. It offers a systematic and precise exposition of classical logic with many examples and exercises, and only the necessary minimum of theory. The book explains the grammar, semantics and use of classical logical languages and teaches the reader how grasp the meaning and translate them to and from natural language. It illustrates with extensive examples the use of the most popular deductive systems -- axiomatic systems, semantic tableaux, natural deduction, and resolution -- for formalising and automating logical reasoning both on propositional and on first-order level, and provides the reader with technical skills needed for practical derivations in them. Systematic guidelines are offered on how to perform logically correct and well-structured reasoning using these deductive systems and the reasoning techniques that they employ. •Concise and systematic exposition, with semi-formal but rigorous treatment of the minimum necessary theory, amply illustrated with examples •Emphasis both on conceptual understanding and on developing practical skills •Solid and balanced coverage of syntactic, semantic, and deductive aspects of logic •Includes extensive sets of exercises, many of them provided with solutions or answers •Supplemented by a website including detailed slides, additional exercises and solutions For more information browse the book's website at: https://logicasatool.wordpress.com
Book Synopsis Kurt Gödel and the Foundations of Mathematics by : Matthias Baaz
Download or read book Kurt Gödel and the Foundations of Mathematics written by Matthias Baaz and published by Cambridge University Press. This book was released on 2011-06-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.
Download or read book Philosophy of Logic written by and published by Elsevier. This book was released on 2006-11-29 with total page 1219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert’s program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights. - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic - Useful bibliographies in every chapter
Download or read book Alan Turing written by S. Barry Cooper and published by Elsevier. This book was released on 2013-03-18 with total page 937 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP, readers will find many of the most significant contributions from the four-volume set of the Collected Works of A. M. Turing. These contributions, together with commentaries from current experts in a wide spectrum of fields and backgrounds, provide insight on the significance and contemporary impact of Alan Turing's work. Offering a more modern perspective than anything currently available, Alan Turing: His Work and Impact gives wide coverage of the many ways in which Turing's scientific endeavors have impacted current research and understanding of the world. His pivotal writings on subjects including computing, artificial intelligence, cryptography, morphogenesis, and more display continued relevance and insight into today's scientific and technological landscape. This collection provides a great service to researchers, but is also an approachable entry point for readers with limited training in the science, but an urge to learn more about the details of Turing's work. 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP Named a 2013 Notable Computer Book in Computing Milieux by Computing Reviews Affordable, key collection of the most significant papers by A.M. Turing Commentary explaining the significance of each seminal paper by preeminent leaders in the field Additional resources available online
Book Synopsis Automated Reasoning by : Christoph Benzmüller
Download or read book Automated Reasoning written by Christoph Benzmüller and published by Springer Nature. This book was released on with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Brief History of Computing by : Gerard O'Regan
Download or read book A Brief History of Computing written by Gerard O'Regan and published by Springer Science & Business Media. This book was released on 2012-03-05 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lively and fascinating text traces the key developments in computation – from 3000 B.C. to the present day – in an easy-to-follow and concise manner. Topics and features: ideal for self-study, offering many pedagogical features such as chapter-opening key topics, chapter introductions and summaries, exercises, and a glossary; presents detailed information on major figures in computing, such as Boole, Babbage, Shannon, Turing, Zuse and Von Neumann; reviews the history of software engineering and of programming languages, including syntax and semantics; discusses the progress of artificial intelligence, with extension to such key disciplines as philosophy, psychology, linguistics, neural networks and cybernetics; examines the impact on society of the introduction of the personal computer, the World Wide Web, and the development of mobile phone technology; follows the evolution of a number of major technology companies, including IBM, Microsoft and Apple.
Download or read book Arguing A.I. written by Sam Williams and published by AtRandom. This book was released on 2002-03-05 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Few scientific topics since the theory of biological evolution have inspired as much controversy as artificial intelligence has. Even now, fifty years after the term first made its appearance in academic journals, many philosophers and more than a few prominent scientists and software programmers dismiss the pursuit of thinking machines as the modern-day equivalent of medieval alchemists’ hunt for the philosopher’s stone-a pursuit based more on faith than on skeptical inquiry. In Arguing A.I., journalist Sam Williams charts both the history of artificial intelligence from its scientific and philosophical roots and the history of the A.I. debate. He examines how and why the tenor of the debate has changed over the last half-decade in particular, as scientists are struggling to take into account the latest breakthroughs in computer science, information technology, and human biology. For every voice predicting machines like 2001’s HAL within the next twenty to thirty years, others have emerged with more pessimistic forecasts. From artificial intelligence’s pioneers John McCarthy and Marvin Minsky, to futurist authors Ray Kurzweil and Hans Moravec, to software architects Bill Joy and Jaron Lanier, Arguing A.I. introduces readers to the people participating in the current debate, both proponents and critics of A.I. who are changing the way computers “think” and the way we think about computers. Ultimately, Arguing A.I. is as much a history of thought as it is a history of science. Williams notes that many of the questions plaguing modern scientists and software programmers are the same questions that have concerned scientists and philosophers since time immemorial: What are the fundamental limitations of science and scientific inquiry? What is the nature of intelligence? And, most important, what does it really mean to be human?
Book Synopsis On Formally Undecidable Propositions of Principia Mathematica and Related Systems by : Kurt Gödel
Download or read book On Formally Undecidable Propositions of Principia Mathematica and Related Systems written by Kurt Gödel and published by Courier Corporation. This book was released on 2012-05-24 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
Book Synopsis Applied Logic for Computer Scientists by : Mauricio Ayala-Rincón
Download or read book Applied Logic for Computer Scientists written by Mauricio Ayala-Rincón and published by Springer. This book was released on 2017-02-04 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to logic and mathematical induction which are the basis of any deductive computational framework. A strong mathematical foundation of the logical engines available in modern proof assistants, such as the PVS verification system, is essential for computer scientists, mathematicians and engineers to increment their capabilities to provide formal proofs of theorems and to certify the robustness of software and hardware systems. The authors present a concise overview of the necessary computational and mathematical aspects of ‘logic’, placing emphasis on both natural deduction and sequent calculus. Differences between constructive and classical logic are highlighted through several examples and exercises. Without neglecting classical aspects of computational logic, the authors also highlight the connections between logical deduction rules and proof commands in proof assistants, presenting simple examples of formalizations of the correctness of algebraic functions and algorithms in PVS. Applied Logic for Computer Scientists will not only benefit students of computer science and mathematics but also software, hardware, automation, electrical and mechatronic engineers who are interested in the application of formal methods and the related computational tools to provide mathematical certificates of the quality and accuracy of their products and technologies.
