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Author | : Donald MacKenzie |
Publisher | : MIT Press |
Total Pages | : 448 |
Release | : 2004-01-30 |
Genre | : Social Science |
ISBN | : 9780262632959 |
Download Mechanizing Proof Book in PDF, ePub and Kindle
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.
Author | : Gianluigi Bellin |
Publisher | : |
Total Pages | : 494 |
Release | : 1990 |
Genre | : Computers |
ISBN | : |
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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)."
Author | : S.R. Buss |
Publisher | : Elsevier |
Total Pages | : 823 |
Release | : 1998-07-09 |
Genre | : Mathematics |
ISBN | : 0080533183 |
Download Handbook of Proof Theory Book in PDF, ePub and Kindle
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.
Author | : A. S. Troelstra |
Publisher | : Cambridge University Press |
Total Pages | : 436 |
Release | : 2000-07-27 |
Genre | : Computers |
ISBN | : 9780521779111 |
Download Basic Proof Theory Book in PDF, ePub and Kindle
This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.
Author | : N. Shankar |
Publisher | : Cambridge University Press |
Total Pages | : 224 |
Release | : 1997-01-30 |
Genre | : Computers |
ISBN | : 9780521585330 |
Download Metamathematics, Machines and Gödel's Proof Book in PDF, ePub and Kindle
Describes the use of computer programs to check several proofs in the foundations of mathematics.
Author | : W. Snyder |
Publisher | : Springer Science & Business Media |
Total Pages | : 181 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 1461204356 |
Download A Proof Theory for General Unification Book in PDF, ePub and Kindle
In this monograph we study two generalizations of standard unification, E-unification and higher-order unification, using an abstract approach orig inated by Herbrand and developed in the case of standard first-order unifi cation by Martelli and Montanari. The formalism presents the unification computation as a set of non-deterministic transformation rules for con verting a set of equations to be unified into an explicit representation of a unifier (if such exists). This provides an abstract and mathematically elegant means of analysing the properties of unification in various settings by providing a clean separation of the logical issues from the specification of procedural information, and amounts to a set of 'inference rules' for unification, hence the title of this book. We derive the set of transformations for general E-unification and higher order unification from an analysis of the sense in which terms are 'the same' after application of a unifying substitution. In both cases, this results in a simple extension of the set of basic transformations given by Herbrand Martelli-Montanari for standard unification, and shows clearly the basic relationships of the fundamental operations necessary in each case, and thus the underlying structure of the most important classes of term unifi cation problems.
Author | : |
Publisher | : BRILL |
Total Pages | : 267 |
Release | : 2023-03-13 |
Genre | : Language Arts & Disciplines |
ISBN | : 9004457429 |
Download Mechanization of Reasoning in a Historical Perspective Book in PDF, ePub and Kindle
This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being. The study which resulted in this volume was carried out in the Historical Section of the research project Logical Systems and Algorithms for Automatic Testing of Reasoning, 1986-1990, in which participated nine Polish universities; the project was coordinated by the Department of Logic, Methodology and Philosophy of Science of the Bia??l??ystok Branch of the University of Warsaw, and supported by the Ministry of Education (some of its results are reported in (Srzednicki (Ed.) 1987). The major part of the project was focussed on the software for computer-aided theorem proving called Mizar MSE (Multi-Sorted first-order logic with Equality, reported in (Marciszewski 1994a)) due to Dr. Andrzej Trybulec. He and other colleagues deserve a grateful mention for a hands-on experience and theoretical stimulants owed to their collaboration.
Author | : Ofer Arieli |
Publisher | : Springer Nature |
Total Pages | : 369 |
Release | : 2021-07-30 |
Genre | : Philosophy |
ISBN | : 3030712583 |
Download Arnon Avron on Semantics and Proof Theory of Non-Classical Logics Book in PDF, ePub and Kindle
This book is a collection of contributions honouring Arnon Avron’s seminal work on the semantics and proof theory of non-classical logics. It includes presentations of advanced work by some of the most esteemed scholars working on semantic and proof-theoretical aspects of computer science logic. Topics in this book include frameworks for paraconsistent reasoning, foundations of relevance logics, analysis and characterizations of modal logics and fuzzy logics, hypersequent calculi and their properties, non-deterministic semantics, algebraic structures for many-valued logics, and representations of the mechanization of mathematics. Avron’s foundational and pioneering contributions have been widely acknowledged and adopted by the scientific community. His research interests are very broad, spanning over proof theory, automated reasoning, non-classical logics, foundations of mathematics, and applications of logic in computer science and artificial intelligence. This is clearly reflected by the diversity of topics discussed in the chapters included in this book, all of which directly relate to Avron’s past and present works. This book is of interest to computer scientists and scholars of formal logic.
Author | : Wolfram Pohlers |
Publisher | : |
Total Pages | : 213 |
Release | : 1989 |
Genre | : |
ISBN | : |
Download Proof Theory Book in PDF, ePub and Kindle
Author | : N. Shankar |
Publisher | : Cambridge University Press |
Total Pages | : 218 |
Release | : 1994-05-12 |
Genre | : Computers |
ISBN | : 9780521420273 |
Download Metamathematics, Machines and Gödel's Proof Book in PDF, ePub and Kindle
The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While Gödel's first incompleteness theorem showed that no computer program could automatically prove certain true theorems in mathematics, the advent of electronic computers and sophisticated software means in practice there are many quite effective systems for automated reasoning that can be used for checking mathematical proofs. This book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including those of Gödel and Church-Rosser. The computer verification using the Boyer-Moore theorem prover yields precise and rigorous proofs of these difficult theorems. It also demonstrates the range and power of automated proof checking technology. The mechanization of metamathematics itself has important implications for automated reasoning, because metatheorems can be applied as labor-saving devices to simplify proof construction.