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Realizability An Introduction To Its Categorical Side

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Realizability

Realizability Book
Author : Jaap van Oosten
Publisher : Elsevier
Release : 2008-04-10
ISBN : 9780080560069
Language : En, Es, Fr & De

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Book Description :

Aimed at starting researchers in the field, Realizability gives a rigorous, yet reasonable introduction to the basic concepts of a field which has passed several successive phases of abstraction. Material from previously unpublished sources such as Ph.D. theses, unpublished papers, etc. has been molded into one comprehensive presentation of the subject area. - The first book to date on this subject area - Provides an clear introduction to Realizability with a comprehensive bibliography - Easy to read and mathematically rigorous - Written by an expert in the field

Theory and Applications of Models of Computation

Theory and Applications of Models of Computation Book
Author : T.V. Gopal,Gerhard Jäger,Silvia Steila
Publisher : Springer
Release : 2017-04-13
ISBN : 3319559117
Language : En, Es, Fr & De

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Book Description :

This book constitutes the refereed proceedings of the 14th Annual Conference on Theory and Applications of Models of Computation, TAMC 2017, held in Bern, Switzerland, in April 2017. The 45 revised full papers presented together with 4 invited papers were carefully reviewed and selected from 103 submissions. The main themes of TAMC 2017 have been computability, computer science logic, complexity, algorithms, and models of computation and systems theory.

Concepts of Proof in Mathematics Philosophy and Computer Science

Concepts of Proof in Mathematics  Philosophy  and Computer Science Book
Author : Dieter Probst,Peter Schuster
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2016-07-25
ISBN : 150150262X
Language : En, Es, Fr & De

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Book Description :

A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.

Sets Models and Proofs

Sets  Models and Proofs Book
Author : Ieke Moerdijk,Jaap van Oosten
Publisher : Springer
Release : 2018-11-23
ISBN : 3319924141
Language : En, Es, Fr & De

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Book Description :

This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.

A Computable Universe

A Computable Universe Book
Author : Hector Zenil
Publisher : World Scientific
Release : 2013
ISBN : 981437430X
Language : En, Es, Fr & De

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Book Description :

This volume, with a foreword by Sir Roger Penrose, discusses the foundations of computation in relation to nature.It focuses on two main questions: What is computation? How does nature compute?The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and philosophical implications.The volume provides a state-of-the-art collection of technical papers and non-technical essays, representing a field that assumes information and computation to be key in understanding and explaining the basic structure underpinning physical reality. It also includes a new edition of Konrad Zuse''s OC Calculating SpaceOCO (the MIT translation), and a panel discussion transcription on the topic, featuring worldwide experts in quantum mechanics, physics, cognition, computation and algorithmic complexity.The volume is dedicated to the memory of Alan M Turing OCo the inventor of universal computation, on the 100th anniversary of his birth, and is part of the Turing Centenary celebrations.

Telos

Telos Book
Author : N.A
Publisher :
Release : 1975
ISBN :
Language : En, Es, Fr & De

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Book Description :

Principles of Ethical Economy

Principles of Ethical Economy Book
Author : P. Koslowski
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 9401009562
Language : En, Es, Fr & De

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Book Description :

John Maynard Keynes wrote to his grandchildren more than fifty years ago about their economic possibilities, and thus about our own: "I see us free, there fore, to return to some of the most sure and certain principles of religion and traditional virtue - that avarice is a vice, that the exaction of usury is a misde meanour. . . . We shall once more value ends above means and prefer the good to the useful" ("Economic Possibilities for Our Grandchildren," pp. 371-72). In the year 1930 Keynes regarded these prospects as realizable only after a time span ofone hundred years, ofwhich we have now achieved more than half. The pres ent book does not share Keynes's view that the possibility of an integration of ethics and economics is dependent exclusively on the state of economic devel opment, though this integration is certainly made easier by an advantageous total economic situation. The conditions of an economy that is becoming post of ethics, cultural industrial and post-modern are favorable for the unification theory, and economics. Economic development makes a new establishment of economic ethics and a theory ofethical economy necessary. Herdecke and Hanover, October 1987 P. K. TABLE OF CONTENTS Foreword v Introduction . 0. 1. Ethical Economy and Political Economy . . 0. 1. 1. Ethical Economy as Theory ofthe Ethical Presuppositions of the Economy and Economic Ethics 3 0. 1. 2.