Probability Theory PDF Download

Author:
Publisher: Allied Publishers
ISBN: 9788177644517
Category :
Languages : en
Pages : 436

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Probability theory

Author: Itamar Pitowsky
Publisher:
ISBN: 9783662137345
Category :
Languages : en
Pages : 224

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Author: Theodore Hailperin
Publisher: Rowman & Littlefield
ISBN: 1611460107
Category : Mathematics
Languages : en
Pages : 124

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Book Description
The present study is an extension of the topic introduced in Dr. Hailperin's Sentential Probability Logic, where the usual true-false semantics for logic is replaced with one based more on probability, and where values ranging from 0 to 1 are subject to probability axioms. Moreover, as the word "sentential" in the title of that work indicates, the language there under consideration was limited to sentences constructed from atomic (not inner logical components) sentences, by use of sentential connectives ("no," "and," "or," etc.) but not including quantifiers ("for all," "there is"). An initial introduction presents an overview of the book. In chapter one, Halperin presents a summary of results from his earlier book, some of which extends into this work. It also contains a novel treatment of the problem of combining evidence: how does one combine two items of interest for a conclusion-each of which separately impart a probability for the conclusion-so as to have a probability for the conclusion basedon taking both of the two items of interest as evidence? Chapter two enlarges the Probability Logic from the first chapter in two respects: the language now includes quantifiers ("for all," and "there is") whose variables range over atomic sentences, notentities as with standard quantifier logic. (Hence its designation: ontological neutral logic.) A set of axioms for this logic is presented. A new sentential notion-the suppositional-in essence due to Thomas Bayes, is adjoined to this logic that later becomes the basis for creating a conditional probability logic. Chapter three opens with a set of four postulates for probability on ontologically neutral quantifier language. Many properties are derived and a fundamental theorem is proved, namely, for anyprobability model (assignment of probability values to all atomic sentences of the language) there will be a unique extension of the probability values to all closed sentences of the language. The chapter concludes by showing the Borel's early denumerableprobability concept (1909) can be justified by its being, in essence, close to Hailperin's probability result applied to denumerable language. The final chapter introduces the notion of conditional-probability to a language having quantifiers of the kind

Author: Zoran Ognjanović
Publisher: Springer
ISBN: 3319470124
Category : Mathematics
Languages : en
Pages : 224

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The aim of this book is to provide an introduction to probability logic-based formalization of uncertain reasoning. The authors' primary interest is mathematical techniques for infinitary probability logics used to obtain results about proof-theoretical and model-theoretical issues such as axiomatizations, completeness, compactness, and decidability, including solutions of some problems from the literature. An extensive bibliography is provided to point to related work, and this book may serve as a basis for further research projects, as a reference for researchers using probability logic, and also as a textbook for graduate courses in logic.

Author: George Boole
Publisher: Courier Corporation
ISBN: 0486488268
Category : Mathematics
Languages : en
Pages : 514

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Authoritative account of the development of Boole's ideas in logic and probability theory ranges from The Mathematical Analysis of Logic to the end of his career. The Laws of Thought formed the most systematic statement of Boole's theories; this volume contains incomplete studies intended for a follow-up volume. 1952 edition.

Author: Rolf Haenni
Publisher: Springer Science & Business Media
ISBN: 9400700083
Category : Science
Languages : en
Pages : 154

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While probabilistic logics in principle might be applied to solve a range of problems, in practice they are rarely applied - perhaps because they seem disparate, complicated, and computationally intractable. This programmatic book argues that several approaches to probabilistic logic fit into a simple unifying framework in which logically complex evidence is used to associate probability intervals or probabilities with sentences. Specifically, Part I shows that there is a natural way to present a question posed in probabilistic logic, and that various inferential procedures provide semantics for that question, while Part II shows that there is the potential to develop computationally feasible methods to mesh with this framework. The book is intended for researchers in philosophy, logic, computer science and statistics. A familiarity with mathematical concepts and notation is presumed, but no advanced knowledge of logic or probability theory is required.

Author: Ian Hacking
Publisher: Cambridge University Press
ISBN: 9780521775014
Category : Mathematics
Languages : en
Pages : 326

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Book Description
An introductory 2001 textbook on probability and induction written by a foremost philosopher of science.

Author: Theodore Hailperin
Publisher: Lehigh University Press
ISBN: 9780934223454
Category : Mathematics
Languages : en
Pages : 316

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Book Description
This study presents a logic in which probability values play a semantic role comparable to that of truth values in conventional logic. The difference comes in with the semantic definition of logical consequence. It will be of interest to logicians, both philosophical and mathematical, and to investigators making use of logical inference under uncertainty, such as in operations research, risk analysis, artificial intelligence, and expert systems.

Author: Henry Ely Kyburg
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 294

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Author: Timothy J. Ross
Publisher: SIAM
ISBN: 0898715253
Category : Mathematics
Languages : en
Pages : 424

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Shows both the shortcomings and benefits of each technique, and even demonstrates useful combinations of the two.