Computation, Proof, Machine - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computation, Proof, Machine write by Gilles Dowek. This book was released on 2015-05-05. Computation, Proof, Machine available in PDF, EPUB and Kindle. Computation is revolutionizing our world, even the inner world of the 'pure' mathematician. Mathematical methods - especially the notion of proof - that have their roots in classical antiquity have seen a radical transformation since the 1970s, as successive advances have challenged the priority of reason over computation. Like many revolutions, this one comes from within. Computation, calculation, algorithms - all have played an important role in mathematical progress from the beginning - but behind the scenes, their contribution was obscured in the enduring mathematical literature. To understand the future of mathematics, this fascinating book returns to its past, tracing the hidden history that follows the thread of computation. Along the way it invites us to reconsider the dialog between mathematics and the natural sciences, as well as the relationship between mathematics and computer science. It also sheds new light on philosophical concepts, such as the notions of analytic and synthetic judgment. Finally, it brings us to the brink of the new age, in which machine intelligence offers new ways of solving mathematical problems previously inaccessible. This book is the 2007 winner of the Grand Prix de Philosophie de l'Académie Française.
Computation, Proof, Machine
Computation, Proof, Machine - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computation, Proof, Machine write by Gilles Dowek. This book was released on 2015-05-05. Computation, Proof, Machine available in PDF, EPUB and Kindle. Computation, calculation, algorithms - all have played an important role in mathematical progress from the beginning - but behind the scenes, their contribution was obscured in the enduring mathematical literature. To understand the future of mathematics, this fascinating book returns to its past, tracing the hidden history that follows the thread of computation.
Logic and Computation
Logic and Computation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Logic and Computation write by Lawrence C. Paulson. This book was released on 1987. Logic and Computation available in PDF, EPUB and Kindle. This book is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines the methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of program statements. Cambridge LCF is based on an earlier theorem-proving system, Edinburgh LCF, which introduced a design that gives the user flexibility to use and extend the system. A goal of this book is to explain the design, which has been adopted in several other systems. The book consists of two parts. Part I outlines the mathematical preliminaries, elementary logic and domain theory, and explains them at an intuitive level, giving reference to more advanced reading; Part II provides sufficient detail to serve as a reference manual for Cambridge LCF. It will also be a useful guide for implementors of other programs based on the LCF approach.
Proofs and Computations
Proofs and Computations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proofs and Computations write by Helmut Schwichtenberg. This book was released on 2011-12-15. Proofs and Computations available in PDF, EPUB and Kindle. Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.
A Machine Program for Theorem-proving
A Machine Program for Theorem-proving - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Machine Program for Theorem-proving write by Martin Davis. This book was released on 1961. A Machine Program for Theorem-proving available in PDF, EPUB and Kindle. The programming of a proof procedure is discussed in connection with trial runs and possible improvements. (Author).
