Author: Egon Börger
Publisher: Springer Science & Business Media
ISBN: 9783540423249
Category : Mathematics
Languages : en
Pages : 500
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Book Description
This book offers a comprehensive treatment of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. The text presents a revealing analysis of the natural order of decidable and undecidable cases and includes a number of simple proofs and exercises.
Author: Börger
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Egon Börger
Publisher: Springer
ISBN: 9783642592072
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book offers a comprehensive treatment of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. The text presents a revealing analysis of the natural order of decidable and undecidable cases and includes a number of simple proofs and exercises.
Author: Duncan L. Dieterly
Publisher:
ISBN:
Category : Decision making
Languages : en
Pages : 26
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Book Description
Author: Roman Murawski
Publisher: Springer Science & Business Media
ISBN: 9401728666
Category : Philosophy
Languages : en
Pages : 416
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Book Description
Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.
Author: David Wallace
Publisher: OUP Oxford
ISBN: 0191057398
Category : Philosophy
Languages : en
Pages : 547
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Book Description
The Emergent Multiverse presents a striking new account of the 'many worlds' approach to quantum theory. The point of science, it is generally accepted, is to tell us how the world works and what it is like. But quantum theory seems to fail to do this: taken literally as a theory of the world, it seems to make crazy claims: particles are in two places at once; cats are alive and dead at the same time. So physicists and philosophers have often been led either to give up on the idea that quantum theory describes reality, or to modify or augment the theory. The Everett interpretation of quantum mechanics takes the apparent craziness seriously, and asks, 'what would it be like if particles really were in two places at once, if cats really were alive and dead at the same time'? The answer, it turns out, is that if the world were like that—if it were as quantum theory claims—it would be a world that, at the macroscopic level, was constantly branching into copies—hence the more sensationalist name for the Everett interpretation, the 'many worlds theory'. But really, the interpretation is not sensationalist at all: it simply takes quantum theory seriously, literally, as a description of the world. Once dismissed as absurd, it is now accepted by many physicists as the best way to make coherent sense of quantum theory. David Wallace offers a clear and up-to-date survey of work on the Everett interpretation in physics and in philosophy of science, and at the same time provides a self-contained and thoroughly modern account of it—an account which is accessible to readers who have previously studied quantum theory at undergraduate level, and which will shape the future direction of research by leading experts in the field.
Author: James Burton
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Prakash Gorroochurn
Publisher: John Wiley & Sons
ISBN: 1118063252
Category : Mathematics
Languages : en
Pages : 341
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Book Description
Winner of the 2012 PROSE Award for Mathematics from The American Publishers Awards for Professional and Scholarly Excellence. "A great book, one that I will certainly add to my personal library." —Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire Classic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature. From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713 Golden Theorem to Parrondo's 1996 Perplexing Paradox, the book clearly outlines the puzzles and problems of probability, interweaving the discussion with rich historical detail and the story of how the mathematicians involved arrived at their solutions. Each problem is given an in-depth treatment, including detailed and rigorous mathematical proofs as needed. Some of the fascinating topics discussed by the author include: Buffon's Needle problem and its ingenious treatment by Joseph Barbier, culminating into a discussion of invariance Various paradoxes raised by Joseph Bertrand Classic problems in decision theory, including Pascal's Wager, Kraitchik's Neckties, and Newcomb's problem The Bayesian paradigm and various philosophies of probability Coverage of both elementary and more complex problems, including the Chevalier de Méré problems, Fisher and the lady testing tea, the birthday problem and its various extensions, and the Borel-Kolmogorov paradox Classic Problems of Probability is an eye-opening, one-of-a-kind reference for researchers and professionals interested in the history of probability and the varied problem-solving strategies employed throughout the ages. The book also serves as an insightful supplement for courses on mathematical probability and introductory probability and statistics at the undergraduate level.
Author: Atanu Sengupta
Publisher: Springer Science & Business Media
ISBN: 3540899146
Category : Mathematics
Languages : en
Pages : 168
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Book Description
In conventional mathematical programming, coefficients of problems are usually determined by the experts as crisp values in terms of classical mathematical reasoning. But in reality, in an imprecise and uncertain environment, it will be utmost unrealistic to assume that the knowledge and representation of an expert can come in a precise way. The wider objective of the book is to study different real decision situations where problems are defined in inexact environment. Inexactness are mainly generated in two ways – (1) due to imprecise perception and knowledge of the human expert followed by vague representation of knowledge as a DM; (2) due to huge-ness and complexity of relations and data structure in the definition of the problem situation. We use interval numbers to specify inexact or imprecise or uncertain data. Consequently, the study of a decision problem requires answering the following initial questions: How should we compare and define preference ordering between two intervals?, interpret and deal inequality relations involving interval coefficients?, interpret and make way towards the goal of the decision problem? The present research work consists of two closely related fields: approaches towards defining a generalized preference ordering scheme for interval attributes and approaches to deal with some issues having application potential in many areas of decision making.
Author: Eric Schechter
Publisher: Princeton University Press
ISBN: 9780691122793
Category : Mathematics
Languages : en
Pages : 530
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Book Description
Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).
