The Collected Works Of Alonzo Church

Author : Tyler Burge,Herbert Enderton
Publisher : MIT Press
Page : 0 pages
File Size : 49,5 Mb
Release : 2019-04-23
Category : Philosophy
ISBN : 9780262025645

Get Book

The Collected Works of Alonzo Church by Tyler Burge,Herbert Enderton Pdf

Writings, including articles, letters, and unpublished work, by one of the twentieth century's most influential figures in mathematical logic and philosophy.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to his important and authoritative textbook Introduction to Mathematical Logic, a substantial amount of previously unpublished work (including chapters for the unfinished second volume of Introduction to Mathematical Logic), and a selection of letters to such correspondents as Rudolf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 With the exception of the reviews, letters, and unpublished work, these appear in chronological order, for the most part in the format in which they were originally published.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.

Author : Alonzo Church
Publisher : Princeton University Press
Page : 396 pages
File Size : 49,9 Mb
Release : 1996
Category : Mathematics
ISBN : 0691029067

Get Book

Introduction to Mathematical Logic by Alonzo Church Pdf

A classic account of mathematical logic from a pioneering giant in the field Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today. Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic. Church was one of the principal founders of the Association for Symbolic Logic; he founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979. At his death in 1995, Church was still regarded as the greatest mathematical logician in the world.

Author : Andrew W. Appel
Publisher : Princeton University Press
Page : 160 pages
File Size : 53,5 Mb
Release : 2014-11-16
Category : Computers
ISBN : 9780691164731

Get Book

Alan Turing's Systems of Logic by Andrew W. Appel Pdf

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.

Author : Kurt Gödel
Publisher : Oxford University Press
Page : 692 pages
File Size : 42,9 Mb
Release : 1986
Category : Biography & Autobiography
ISBN : 0198500734

Get Book

Kurt Gödel: Collected Works: Volume IV by Kurt Gödel Pdf

Kurt Gödel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gödel's writings. The first three volumes, already published, consist of the papers and essays of Gödel. The final two volumes of the set deal with Gödel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

Author : Anonim
Publisher : Universal-Publishers
Page : 179 pages
File Size : 46,7 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9781612339511

Get Book

Proof in Alonzo Church's and Alan Turing's Mathematical Logic: Undecidability of First Order Logic by Anonim Pdf

Author : Alfred North Whitehead,Bertrand Russell
Publisher : Cambridge University Press
Page : 524 pages
File Size : 50,8 Mb
Release : 1927
Category : Mathematics
ISBN : 052106791X

Get Book

Principia Mathematica by Alfred North Whitehead,Bertrand Russell Pdf

The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.

Author : Andrew Bacon
Publisher : Taylor & Francis
Page : 483 pages
File Size : 50,7 Mb
Release : 2023-09-29
Category : Philosophy
ISBN : 9781000925753

Get Book

A Philosophical Introduction to Higher-order Logics by Andrew Bacon Pdf

This is the first comprehensive textbook on higher-order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages—their model theory and proof theory, the theory of λ-abstraction and its generalizations—and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making it more appropriate for foundational metaphysics than other introductions to the subject from computer science, mathematics, and linguistics. A Philosophical Introduction to Higher-order Logics assumes only that readers have a basic knowledge of first-order logic. With an emphasis on exercises, it can be used as a textbook though is also ideal for self-study. Author Andrew Bacon organizes the book's 18 chapters around four main parts: I. Typed Language II. Higher-Order Languages III. General Higher-Order Languages IV. Higher-Order Model Theory In addition, two appendices cover the Curry-Howard isomorphism and its applications for modeling propositional structure. Each chapter includes exercises that move from easier to more difficult, strategically placed throughout the chapter, and concludes with an annotated suggested reading list providing graduate students with most valuable additional resources. Key Features: Is the first comprehensive introduction to higher-order logic as a grounding for addressing problems in metaphysics Introduces the basic formal tools that are needed to theorize in, and model, higher-order languages Offers an abundance of - Simple exercises throughout the book, serving as comprehension checks on basic concepts and definitions - More difficult exercises designed to facilitate long-term learning Contains annotated sections on further reading, pointing the reader to related literature, learning resources, and historical context

Author : S. Barry Cooper,J. van Leeuwen
Publisher : Elsevier
Page : 944 pages
File Size : 50,8 Mb
Release : 2013-03-18
Category : Mathematics
ISBN : 9780123870124

Get Book

Alan Turing: His Work and Impact by S. Barry Cooper,J. van Leeuwen Pdf

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

Author : Tyler Burge
Publisher : Clarendon Press
Page : 434 pages
File Size : 43,9 Mb
Release : 2005-02-17
Category : Philosophy
ISBN : 0191557382

Get Book

Truth, Thought, Reason by Tyler Burge Pdf

Tyler Burge presents a collection of his seminal essays on Gottlob Frege (1848-1925), who has a strong claim to be seen as the founder of modern analytic philosophy, and whose work remains at the centre of philosophical debate today. Truth, Thought, Reason gathers some of Burge's most influential work from the last twenty-five years, and also features important new material, including a substantial introduction and postscripts to four of the ten papers. It will be an essential resource for any historian of modern philosophy, and for anyone working on philosophy of language, epistemology, or philosophical logic.

Author : Frederique Janssen-Lauret
Publisher : Oxford University Press
Page : 321 pages
File Size : 48,5 Mb
Release : 2020-10-22
Category : Philosophy
ISBN : 9780192609878

Get Book

Quine, Structure, and Ontology by Frederique Janssen-Lauret Pdf

W.V. Quine, a champion of philosophical naturalism and pioneer of mathematical logic, was one of the most important philosophers of the 20th century. Contemporary thought in ontology, epistemology, and the philosophy of logic and language owes much to his influence, yet recent work in these areas has become increasingly dismissive of his views. This is often because of mistaken or overly simplified conceptions of his philosophy which overlook the development of his views over time, in particular the growing importance of a kind of structuralism to his system as it evolved. This volume provides a fuller, richer picture of Quine's views and their development. With contributions from leading philosophers in a range of subfields including philosophical logic, philosophy of language, history of philosophy, mathematics, philosophy of time, and set theory, it is the first to investigate Quine's views on structure and how it permeates and shapes his attitude to a range of philosophical questions.

Author : Kurt Gödel
Publisher : Courier Corporation
Page : 82 pages
File Size : 52,7 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9780486158402

Get Book

On Formally Undecidable Propositions of Principia Mathematica and Related Systems by Kurt Gödel Pdf

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.

Author : J. Richard Büchi
Publisher : Springer Science & Business Media
Page : 691 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461389286

Get Book

The Collected Works of J. Richard Büchi by J. Richard Büchi Pdf

J. Richard Biichi is well known for his work in mathematical logic and theoretical computer science. (He himself would have sharply objected to the qualifier "theoretical," because he more or less identified science and theory, using "theory" in a broader sense and "science" in a narrower sense than usual.) We are happy to present here this collection of his papers. I (DS)1 worked with Biichi for many years, on and off, ever since I did my Ph.D. thesis on his Sequential Calculus. His way was to travel locally, not globally: When we met we would try some specific problem, but rarely dis cussed research we had done or might do. After he died in April 1984 I sifted through the manuscripts and notes left behind and was dumbfounded to see what areas he had been in. Essentially I knew about his work in finite au tomata, monadic second-order theories, and computability. But here were at least four layers on his writing desk, and evidently he had been working on them all in parallel. I am sure that many people who knew Biichi would tell an analogous story.

Author : Julia Robinson
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 40,8 Mb
Release : 1996
Category : Mathematics
ISBN : 0821805754

Get Book

The Collected Works of Julia Robinson by Julia Robinson Pdf

This volume presents all the published works -- spanning more than thirty years -- of Julia Bowman Robinson. These papers constitute important contributions to the theory of effectively calculable functions and to its applications. Outstanding among the latter are Robinson's proof of the effective unsolvability of the decision problem for the rational number field (and, consequently of that for the first-order theory of all fields), and her work that provided the central step toward the negative solution of Hilbert's Tenth Problem. These results provide upper bound for what one can hope to obtain in the way of positive solutions to the decision problem for special classes of fields and for special classes of diophantine equations, respectively. Besides thematic unity, Robinson's papers are distinguished by their clarity of purpose and accessibility to non-specialists as well as specialists. The volume also includes an extensive biographical memoir on the life and work of Robinson, who will be remembered not only for her distinctive and vital contributions, but also as the first woman to be elected to the mathematical section of the National Academy of Sciences and as the first woman to be President of the American Mathematical Society.

Author : Alessandro Capone
Publisher : Springer Nature
Page : 296 pages
File Size : 43,6 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9783031501098

Get Book

Philosophy, Cognition and Pragmatics by Alessandro Capone Pdf

Author : Natasha Alechina,Andreas Herzig,Fei Liang
Publisher : Springer Nature
Page : 344 pages
File Size : 51,5 Mb
Release : 2023-10-23
Category : Philosophy
ISBN : 9783031455582

Get Book

Logic, Rationality, and Interaction by Natasha Alechina,Andreas Herzig,Fei Liang Pdf

This LNCS book is part of the FOLLI book series and constitutes the proceedings of the 9th International Workshop on Logic, Rationality, and Interaction, LORI 2023, held in Jinan, China, in October 2023. The 15 full papers presented together with 7 short papers in this book were carefully reviewed and selected from 40 submissions. The workshop covers a wide range on the following topics such as agency; argumentation and agreement; belief representation; probability and uncertainty; belief revision and belief merging; knowledge and action; dynamics of informational attitudes; intentions, plans, and goals; decision making and planning; preference and utility; cooperation; strategic reasoning and game theory; epistemology; social choice; social interaction; speech acts; knowledge representation; norms and normative systems; natural language; rationality; philosophical logic.