Download or read book Mathematics and Plausible Reasoning Two Volumes in One written by George Polya and published by . This book was released on 2014-01 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2014 Reprint of 1954 American Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics." This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can be given, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but no proved until much later. In the same way, solutions to problems can be guessed, and a god guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser."-From the Dust Jacket.
Download or read book Probabilistic Reasoning in Intelligent Systems written by Judea Pearl and published by Elsevier. This book was released on 2014-06-28 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic Reasoning in Intelligent Systems is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertainty--and offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognition--in short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information. Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.
Download or read book Patterns of Plausible Inference written by George Pólya and published by . This book was released on 1954 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. II, on Patterns of Plausible Inference, attempts to develop a logic of plausibility. What makes some evidence stronger and some weaker? How does one seek evidence that will make a suspected truth more probable? These questions involve philosophy and psychology as well as mathematics.
Download or read book Factual and Plausible Reasoning written by David Billington and published by . This book was released on 2019-04-18 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Factual reasoning is reasoning with statements that are certain, called facts. Classical propositional logic is often used for such reasoning. However classical propositional logic has two faults. Its most serious fault is the irrational way it behaves when the statements are inconsistent. The second, less serious, fault is that there is an intuitive understanding of the meaning of 'follows from' that classical propositional logic does not capture. Various new consistent subsets of a set of inconsistent statements are investigated. This yields new more rational propositional logics for factual reasoning that capture the missing intuitive meaning of 'follows from'. Logics that do factual reasoning have properties that can be expressed by using consequence functions. A consequence function is meant to be a function whose input is a set of formulas and whose output is the set of consequences of those formulas. However, there is no adequate definition of what a consequence function is. A new definition of what a consequence function should be is proposed and shown to have many desirable properties. Plausible reasoning is reasoning with statements that are either facts, or are likely, called defeasible statements. Moreover all defeasible statements have the same likelihood; hence there are no numbers, like probabilities, involved. Many principles of plausible reasoning are suggested and several important plausible reasoning examples are considered. A propositional logic is defined that satisfies all the principles and reasons correctly with all the examples. As far as we are aware, this is the only such logic.
Download or read book Mathematics by Experiment written by Jonathan Borwein and published by CRC Press. This book was released on 2008-10-27 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences", that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and insights, Experimentation in Mathematics: Computational P
Download or read book Plausible Reasoning written by Nicholas Rescher and published by . This book was released on 1976 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Probability Theory written by and published by Allied Publishers. This book was released on 2013 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory
Download or read book Reasoning written by Anthony Simon Laden and published by Oxford University Press, USA. This book was released on 2012-05-31 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Anthony Simon Laden explores the kind of reasoning we engage in when we live together: when we are responsive to others and neither commanding nor deferring to them. He argues for a new, social picture of the activity of reasoning, in which reasoning is a species of conversation—social, ongoing, and governed by a set of characteristic norms.
Download or read book Psychology of Reasoning written by Peter Cathcart Wason and published by Harvard University Press. This book was released on 1972 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the core of the "Psychology of Reasoning" is a vigorous discussion that incorporates various illustrations--some of them humorous, all of them fascinating--of the use of reason under a wide variety of different conditions. Particular emphasis is placed on the difficulties involved in dealing with negatively marked information that must be combined and used with other information for reaching conclusions. Thorough treatment is given as well to the search for plausible contexts that will render anomalous or ambiguous statements "sensible."
Download or read book Maximum Entropy and Bayesian Methods in Science and Engineering written by G. Erickson and published by Springer Science & Business Media. This book was released on 1988-08-31 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume has its origin in the Fifth, Sixth and Seventh Workshops on and Bayesian Methods in Applied Statistics", held at "Maximum-Entropy the University of Wyoming, August 5-8, 1985, and at Seattle University, August 5-8, 1986, and August 4-7, 1987. It was anticipated that the proceedings of these workshops would be combined, so most of the papers were not collected until after the seventh workshop. Because all of the papers in this volume are on foundations, it is believed that the con tents of this volume will be of lasting interest to the Bayesian community. The workshop was organized to bring together researchers from different fields to critically examine maximum-entropy and Bayesian methods in science and engineering as well as other disciplines. Some of the papers were chosen specifically to kindle interest in new areas that may offer new tools or insight to the reader or to stimulate work on pressing problems that appear to be ideally suited to the maximum-entropy or Bayesian method. A few papers presented at the workshops are not included in these proceedings, but a number of additional papers not presented at the workshop are included. In particular, we are delighted to make available Professor E. T. Jaynes' unpublished Stanford University Microwave Laboratory Report No. 421 "How Does the Brain Do Plausible Reasoning?" (dated August 1957). This is a beautiful, detailed tutorial on the Cox-Polya-Jaynes approach to Bayesian probability theory and the maximum-entropy principle.
Download or read book Argumentation Schemes for Presumptive Reasoning written by Douglas Walton and published by Routledge. This book was released on 2013-11-05 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent concerns with the evaluation of argumentation in informal logic and speech communication center around nondemonstrative arguments that lead to tentative or defeasible conclusions based on a balance of considerations. Such arguments do not appear to have structures of the kind traditionally identified with deductive and inductive reasoning, but are extremely common and are often called "plausible" or "presumptive," meaning that they are only provisionally acceptable even when they are correct. How is one to judge, by some clearly defined standard, whether such arguments are correct or not in a given instance? The answer lies in what are called argumentation schemes -- forms of argument (structures of inference) that enable one to identify and evaluate common types of argumentation in everyday discourse. This book identifies 25 argumentation schemes for presumptive reasoning and matches a set of critical questions to each. These two elements -- the scheme and the questions -- are then used to evaluate a given argument in a particular case in relation to a context of dialogue in which the argument occurred. In recent writings on argumentation, there is a good deal of stress placed on how important argumentation schemes are in any attempt to evaluate common arguments in everyday reasoning as correct or fallacious, acceptable or questionable. However, the problem is that the literature thus far has not produced a precise and user-friendly enough analysis of the structures of the argumentation schemes themselves, nor have any of the documented accounts been as helpful, accessible, or systematic as they could be, especially in relation to presumptive reasoning. This book solves the problem by presenting the most common presumptive schemes in an orderly and clear way that makes them explicit and useful as precisely defined structures. As such, it will be an indispensable tool for researchers, students, and teachers in the areas of critical thinking, argumentation, speech communication, informal logic, and discourse analysis.
Download or read book The Dialogical Roots of Deduction written by Catarina Dutilh Novaes and published by Cambridge University Press. This book was released on 2020-12-17 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive account of the concept and practices of deduction covering philosophy, history, cognition and mathematical practice.
Download or read book Reasoning About Knowledge written by Ronald Fagin and published by MIT Press. This book was released on 2004-01-09 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reasoning about knowledge—particularly the knowledge of agents who reason about the world and each other's knowledge—was once the exclusive province of philosophers and puzzle solvers. More recently, this type of reasoning has been shown to play a key role in a surprising number of contexts, from understanding conversations to the analysis of distributed computer algorithms. Reasoning About Knowledge is the first book to provide a general discussion of approaches to reasoning about knowledge and its applications to distributed systems, artificial intelligence, and game theory. It brings eight years of work by the authors into a cohesive framework for understanding and analyzing reasoning about knowledge that is intuitive, mathematically well founded, useful in practice, and widely applicable. The book is almost completely self-contained and should be accessible to readers in a variety of disciplines, including computer science, artificial intelligence, linguistics, philosophy, cognitive science, and game theory. Each chapter includes exercises and bibliographic notes.
Download or read book What Is Mathematical Logic written by J. N. Crossley and published by Courier Corporation. This book was released on 2012-08-29 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: A serious introductory treatment geared toward non-logicians, this survey traces the development of mathematical logic from ancient to modern times and discusses the work of Planck, Einstein, Bohr, Pauli, Heisenberg, Dirac, and others. 1972 edition.
Download or read book Experimentation in Mathematics written by Jonathan M. Borwein and published by CRC Press. This book was released on 2004-04-12 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments. The authors address the role of
Download or read book Data and Evidence in Linguistics written by András Kertész and published by Cambridge University Press. This book was released on 2012-02-09 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The question of what types of data and evidence can be used is one of the most important topics in linguistics. This book is the first to comprehensively present the methodological problems associated with linguistic data and evidence. Its originality is twofold. First, the authors' approach accounts for a series of unexplained characteristics of linguistic theorising: the uncertainty and diversity of data, the role of evidence in the evaluation of hypotheses, the problem solving strategies as well as the emergence and resolution of inconsistencies. Second, the findings are obtained by the application of a new model of plausible argumentation which is also of relevance from a general argumentation theoretical point of view. All concepts and theses are systematically introduced and illustrated by a number of examples from different linguistic theories, and a detailed case-study section shows how the proposed model can be applied to specific linguistic problems.
Download or read book Demystifying Legal Reasoning written by Larry Alexander and published by Cambridge University Press. This book was released on 2008-06-16 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demystifying Legal Reasoning defends the proposition that there are no special forms of reasoning peculiar to law. Legal decision makers engage in the same modes of reasoning that all actors use in deciding what to do: open-ended moral reasoning, empirical reasoning, and deduction from authoritative rules. This book addresses common law reasoning when prior judicial decisions determine the law, and interpretation of texts. In both areas, the popular view that legal decision makers practise special forms of reasoning is false.
