Mechanizing Proof
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Mechanizing Proof
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Author : Donald MacKenzie
language : en
Publisher: MIT Press
Release Date : 2004-01-30
Mechanizing Proof written by Donald MacKenzie and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-30 with Social Science categories.
Most aspects of our private and social lives—our safety, the integrity of the financial system, the functioning of utilities and other services, and national security—now depend on computing. But how can we know that this computing is trustworthy? In Mechanizing Proof, Donald MacKenzie addresses this key issue by investigating the interrelations of computing, risk, and mathematical proof over the last half century from the perspectives of history and sociology. His discussion draws on the technical literature of computer science and artificial intelligence and on extensive interviews with participants. MacKenzie argues that our culture now contains two ideals of proof: proof as traditionally conducted by human mathematicians, and formal, mechanized proof. He describes the systems constructed by those committed to the latter ideal and the many questions those systems raise about the nature of proof. He looks at the primary social influence on the development of automated proof—the need to predict the behavior of the computer systems upon which human life and security depend—and explores the involvement of powerful organizations such as the National Security Agency. He concludes that in mechanizing proof, and in pursuing dependable computer systems, we do not obviate the need for trust in our collective human judgment.
Mechanizing Proof Theory
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Author : Gianluigi Bellin
language : en
Publisher:
Release Date : 1990
Mechanizing Proof Theory written by Gianluigi Bellin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Computers categories.
In Part II we study Herbrand's Theorem in Linear Logic and the No Counterexample Interpretation in a fragment of Peano Arithmetic (section 10). As an application to Ramsey Theory we give a parametric form of the Ramsey Theorem, that generalizes the Infinite, the Finite and the Ramsey-Paris-Harrington Theorems for a fixed exponent (sections 10-13)."
Handbook Of Proof Theory
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Author : S.R. Buss
language : en
Publisher: Elsevier
Release Date : 1998-07-09
Handbook Of Proof Theory written by S.R. Buss and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-09 with Mathematics categories.
This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.
Reductive Logic And Proof Search
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Author : David J. Pym
language : en
Publisher: Clarendon Press
Release Date : 2004-04-29
Reductive Logic And Proof Search written by David J. Pym and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-29 with Mathematics categories.
This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and in theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (2nd Edition), Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects , J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning , and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2 .
Burdens Of Proof
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Author : Jean-Francois Blanchette
language : en
Publisher: MIT Press
Release Date : 2012-04-27
Burdens Of Proof written by Jean-Francois Blanchette and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-27 with Computers categories.
An examination of the challenges of establishing the authenticity of electronic documents—in particular the design of a cryptographic equivalent to handwritten signatures. The gradual disappearance of paper and its familiar evidential qualities affects almost every dimension of contemporary life. From health records to ballots, almost all documents are now digitized at some point of their life cycle, easily copied, altered, and distributed. In Burdens of Proof, Jean-François Blanchette examines the challenge of defining a new evidentiary framework for electronic documents, focusing on the design of a digital equivalent to handwritten signatures. From the blackboards of mathematicians to the halls of legislative assemblies, Blanchette traces the path of such an equivalent: digital signatures based on the mathematics of public-key cryptography. In the mid-1990s, cryptographic signatures formed the centerpiece of a worldwide wave of legal reform and of an ambitious cryptographic research agenda that sought to build privacy, anonymity, and accountability into the very infrastructure of the Internet. Yet markets for cryptographic products collapsed in the aftermath of the dot-com boom and bust along with cryptography's social projects. Blanchette describes the trials of French bureaucracies as they wrestled with the application of electronic signatures to real estate contracts, birth certificates, and land titles, and tracks the convoluted paths through which electronic documents acquire moral authority. These paths suggest that the material world need not merely succumb to the virtual but, rather, can usefully inspire it. Indeed, Blanchette argues, in renewing their engagement with the material world, cryptographers might also find the key to broader acceptance of their design goals.
The History Of Mathematical Proof In Ancient Traditions
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Author : Karine Chemla
language : en
Publisher: Cambridge University Press
Release Date : 2012-07-05
The History Of Mathematical Proof In Ancient Traditions written by Karine Chemla 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 2012-07-05 with Philosophy categories.
This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.
Theorem Proving In Higher Order Logics
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Author : Elsa L. Gunter
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-08-06
Theorem Proving In Higher Order Logics written by Elsa L. Gunter 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 1997-08-06 with Computers categories.
This book constitutes the refereed proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics, TPHOLs '97, held in Murray Hill, NJ, USA, in August 1997. The volume presents 19 carefully revised full papers selected from 32 submissions during a thorough reviewing process. The papers cover work related to all aspects of theorem proving in higher order logics, particularly based on secure mechanization of those logics; the theorem proving systems addressed include Coq, HOL, Isabelle, LEGO, and PVS.
Computational Logic
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Author : Dov M. Gabbay
language : en
Publisher: Newnes
Release Date : 2014-12-09
Computational Logic written by Dov M. Gabbay and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-09 with Mathematics categories.
Handbook of the History of Logic brings to the development of logic the best in modern techniques of historical and interpretative scholarship. Computational logic was born in the twentieth century and evolved in close symbiosis with the advent of the first electronic computers and the growing importance of computer science, informatics and artificial intelligence. With more than ten thousand people working in research and development of logic and logic-related methods, with several dozen international conferences and several times as many workshops addressing the growing richness and diversity of the field, and with the foundational role and importance these methods now assume in mathematics, computer science, artificial intelligence, cognitive science, linguistics, law and many engineering fields where logic-related techniques are used inter alia to state and settle correctness issues, the field has diversified in ways that even the pure logicians working in the early decades of the twentieth century could have hardly anticipated. Logical calculi, which capture an important aspect of human thought, are now amenable to investigation with mathematical rigour and computational support and fertilized the early dreams of mechanised reasoning: “Calculemus . The Dartmouth Conference in 1956 – generally considered as the birthplace of artificial intelligence – raised explicitly the hopes for the new possibilities that the advent of electronic computing machinery offered: logical statements could now be executed on a machine with all the far-reaching consequences that ultimately led to logic programming, deduction systems for mathematics and engineering, logical design and verification of computer software and hardware, deductive databases and software synthesis as well as logical techniques for analysis in the field of mechanical engineering. This volume covers some of the main subareas of computational logic and its applications. Chapters by leading authorities in the field Provides a forum where philosophers and scientists interact Comprehensive reference source on the history of logic
Artificial Intelligence Automated Reasoning And Symbolic Computation
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Author : Jacques Calmet
language : en
Publisher: Springer
Release Date : 2003-08-02
Artificial Intelligence Automated Reasoning And Symbolic Computation written by Jacques Calmet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-02 with Computers categories.
This book constitutes the refereed proceedings of the joint International Conferences on Artificial Intelligence and Symbolic Computation, AISC 2002, and Calculemus 2002 held in Marseille, France, in July 2002.The 24 revised full papers presented together with 2 system descriptions were carefully reviewed and selected from 52 submissions. Among the topics covered are automated theorem proving, logical reasoning, mathematical modeling, algebraic computations, computational mathematics, and applications in engineering and industrial practice.
Distributed Computing And Internet Technology
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Author : Dang Van Hung
language : en
Publisher: Springer Nature
Release Date : 2020-01-01
Distributed Computing And Internet Technology written by Dang Van Hung and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-01 with Computers categories.
This book constitutes the proceedings of the 16th International Conference on Distributed Computing and Internet Technology, ICDCIT 2020, held in Bhubaneswar, India, in January 2020. The 20 full and 3 short papers presented in this volume were carefully reviewed and selected from 110 submissions. In addition, the book included 6 invited papers. The contributions were organized in topical sections named: invited talks; concurrent and distributed systems modelling and verification; cloud and grid computing; social networks, machine learning and mobile networks; data processing and blockchain technology; and short papers.