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Booles Logic And Probability
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Book Synopsis Boole's Logic and Probability by : T. Hailperin
Download or read book Boole's Logic and Probability written by T. Hailperin and published by Elsevier. This book was released on 1986-10-01 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition in 1976, there has been a notable increase of interest in the development of logic. This is evidenced by the several conferences on the history of logic, by a journal devoted to the subject, and by an accumulation of new results. This increased activity and the new results - the chief one being that Boole's work in probability is best viewed as a probability logic - were influential circumstances conducive to a new edition. Chapter 1, presenting Boole's ideas on a mathematical treatment of logic, from their emergence in his early 1847 work on through to his immediate successors, has been considerably enlarged. Chapter 2 includes additional discussion of the ``uninterpretable'' notion, both semantically and syntactically. Chapter 3 now includes a revival of Boole's abandoned propositional logic and, also, a discussion of his hitherto unnoticed brush with ancient formal logic. Chapter 5 has an improved explanation of why Boole's probability method works. Chapter 6, Applications and Probability Logic, is a new addition. Changes from the first edition have brought about a three-fold increase in the bibliography.
Book Synopsis Studies in Logic and Probability by : George Boole
Download or read book Studies in Logic and Probability written by George Boole and published by Courier Corporation. This book was released on 2012-01-01 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Logic and Conditional Probability by : Philip Calabrese
Download or read book Logic and Conditional Probability written by Philip Calabrese and published by . This book was released on 2017-10-25 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops an algebra of Boolean fractions, (ab) - ordered pairs of propositions or events - "a if b", "event a given event b". In nine chapters, the author shows that these conditional propositions (together with their associated instantiations or models): Provide logical elements that better represent and more faithfully facilitate manipulation of certain and uncertain conditional information Extend the Boole's algebra of 2-valued statements to a 3-valued system that includes "inapplicable statements" - those whose condition may be false in some or all instances (examples, cases, models...) Allow a definition of the probability of an arbitrary Boolean proposition Non-trivially combine Boolean logic with standard conditional probability theory Provide a complete and adequate development of the crucial 4th operation for Boolean logic, namely conditioning, including iterated conditioning Provide an expanded theory of deduction defined in terms of the extended operations on the Boolean fractions Admit a variety of deduction relations, and that the deductively closed sets generated by some initial set of conditionals can be calculated Extend the ordinary function operations of sum, difference, product & quotient to real-valued functions with possibly different or overlapping domains of definition Represent & simplify complex conditional statements in Bayesian expert systems used to calculate maximum information entropy solutions Explicate the logic of quantum measurements by better expressing the changing conditions in quantum mechanics
Book Synopsis Mathematical Logic and Probability with Basic Programming by : William S. Dorn
Download or read book Mathematical Logic and Probability with Basic Programming written by William S. Dorn and published by . This book was released on 1973 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Sentential Probability Logic by : Theodore Hailperin
Download or read book Sentential Probability Logic written by Theodore Hailperin and published by Lehigh University Press. This book was released on 1996 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Probabilistic Logic in a Coherent Setting by : Giulianella Coletti
Download or read book Probabilistic Logic in a Coherent Setting written by Giulianella Coletti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The approach to probability theory followed in this book (which differs radically from the usual one, based on a measure-theoretic framework) characterizes probability as a linear operator rather than as a measure, and is based on the concept of coherence, which can be framed in the most general view of conditional probability. It is a `flexible' and unifying tool suited for handling, e.g., partial probability assessments (not requiring that the set of all possible `outcomes' be endowed with a previously given algebraic structure, such as a Boolean algebra), and conditional independence, in a way that avoids all the inconsistencies related to logical dependence (so that a theory referring to graphical models more general than those usually considered in bayesian networks can be derived). Moreover, it is possible to encompass other approaches to uncertain reasoning, such as fuzziness, possibility functions, and default reasoning. The book is kept self-contained, provided the reader is familiar with the elementary aspects of propositional calculus, linear algebra, and analysis.
Book Synopsis Logic and Probability in Quantum Mechanics by : Patrick Suppes
Download or read book Logic and Probability in Quantum Mechanics written by Patrick Suppes and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the academic years 1972-1973 and 1973-1974, an intensive sem inar on the foundations of quantum mechanics met at Stanford on a regular basis. The extensive exploration of ideas in the seminar led to the org~ization of a double issue of Synthese concerned with the foundations of quantum mechanics, especially with the role of logic and probability in quantum meChanics. About half of the articles in the volume grew out of this seminar. The remaining articles have been so licited explicitly from individuals who are actively working in the foun dations of quantum mechanics. Seventeen of the twenty-one articles appeared in Volume 29 of Syn these. Four additional articles and a bibliography on -the history and philosophy of quantum mechanics have been added to the present volume. In particular, the articles by Bub, Demopoulos, and Lande, as well as the second article by Zanotti and myself, appear for the first time in the present volume. In preparing the articles for publication I am much indebted to Mrs. Lillian O'Toole, Mrs. Dianne Kanerva, and Mrs. Marguerite Shaw, for their extensive assistance.
Book Synopsis Probability Algebras and Stochastic Spaces by : Demetrios A. Kappos
Download or read book Probability Algebras and Stochastic Spaces written by Demetrios A. Kappos and published by Academic Press. This book was released on 2014-07-03 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability Algebras and Stochastic Spaces explores the fundamental notions of probability theory in the so-called “point-free way. The space of all elementary random variables defined over a probability algebra in a “point-free way is a base for the stochastic space of all random variables, which can be obtained from it by lattice-theoretic extension processes. This book is composed of eight chapters and begins with discussions of the definition, properties, scope, and extension of probability algebras. The succeeding chapters deal with the Cartesian product of probability algebras and the principles of stochastic spaces. These topics are followed by surveys of the expectation, moments, and spaces of random variables. The final chapters define generalized random variables and the Boolean homomorphisms of these variables. This book will be of great value to mathematicians and advance mathematics students.
Book Synopsis Probability Theory on Boolean Algebras of Events by : Octav Onicescu
Download or read book Probability Theory on Boolean Algebras of Events written by Octav Onicescu and published by . This book was released on 1976 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Chance and Structure by : John M. Vickers
Download or read book Chance and Structure written by John M. Vickers and published by . This book was released on 1988 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discussing the relations between logic and probability, this book compares classical 17th- and 18th-century theories of probability with contemporary theories, explores recent logical theories of probability, and offers a new account of probability as a part of logic.
Book Synopsis Information Processing by : David Blower
Download or read book Information Processing written by David Blower and published by Createspace Independent Publishing Platform. This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume I was corrected and revised in September 2017. This book begins the task of defining, explaining, arguing for, and, in the end, providing a rationale for information processing. Volume I is concerned with the notion that an information processor is mainly engaged in making inferences. An information processor would prefer to reach definite conclusions by using some form of deduction. Unfortunately, it is often thwarted in this desire by a fundamental lack of relevant information. Probability theory has developed as a rigorous way of dealing with the uncertainty surrounding inference. Thus, we begin by treating some of the formal manipulation rules that crop up in probability theory. To provide some foundational basis for the applications to appear in later Volumes, the topics of Boolean Algebra, Classical Logic, and Cellular Automata will make an appearance here.
Book Synopsis Boole's Logic and Probability by : Theodore Hailperin
Download or read book Boole's Logic and Probability written by Theodore Hailperin and published by . This book was released on 1976 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Philosophical Lectures on Probability by : Bruno de Finetti
Download or read book Philosophical Lectures on Probability written by Bruno de Finetti and published by Springer Science & Business Media. This book was released on 2008-05-20 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bruno de Finetti (1906–1985) is the founder of the subjective interpretation of probability, together with the British philosopher Frank Plumpton Ramsey. His related notion of “exchangeability” revolutionized the statistical methodology. This book (based on a course held in 1979) explains in a language accessible also to non-mathematicians the fundamental tenets and implications of subjectivism, according to which the probability of any well specified fact F refers to the degree of belief actually held by someone, on the ground of her whole knowledge, on the truth of the assertion that F obtains.
Book Synopsis Boolean Algebra and Its Applications by : J. Eldon Whitesitt
Download or read book Boolean Algebra and Its Applications written by J. Eldon Whitesitt and published by Courier Corporation. This book was released on 2012-05-24 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory treatment begins with set theory and fundamentals of Boolean algebra, proceeding to concise accounts of applications to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. 1961 edition.
Book Synopsis Sets and Boolean Algebra by : Marcel Rueff
Download or read book Sets and Boolean Algebra written by Marcel Rueff and published by Elsevier Publishing Company. This book was released on 1970 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theories of Probability by : Louis Narens
Download or read book Theories of Probability written by Louis Narens and published by World Scientific. This book was released on 2007 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Standard probability theory has been an enormously successful contribution to modern science. However, from many perspectives it is too narrow as a general theory of uncertainty, particularly for issues involving subjective uncertainty. This first-of-its-kind book is primarily based on qualitative approaches to probabilistic-like uncertainty, and includes qualitative theories for the standard theory as well as several of its generalizations.One of these generalizations produces a belief function composed of two functions: a probability function that measures the probabilistic strength of an uncertain event, and another function that measures the amount of ambiguity or vagueness of the event. Another unique approach of the book is to change the event space from a boolean algebra, which is closely linked to classical propositional logic, to a different event algebra that is closely linked to a well-studied generalization of classical propositional logic known as intuitionistic logic. Together, these new qualitative theories succeed where the standard probability theory fails by accounting for a number of puzzling empirical findings in the psychology of human probability judgments and decision making.
Book Synopsis Belief and Probability by : J.M. Vickers
Download or read book Belief and Probability written by J.M. Vickers and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. A WORD ABOUT PRESUPPOSITIONS This book is addressed to philosophers, and not necessarily to those philosophers whose interests and competence are largely mathematical or logical in the formal sense. It deals for the most part with problems in the theory of partial judgment. These problems are naturally formulated in numerical and logical terms, and it is often not easy to formulate them precisely otherwise. Indeed, the involvement of arithmetical and logical concepts seems essential to the philosophies of mind and action at just the point where they become concerned with partial judgment and" belief. I have tried throughout to use no mathematics that is not quite elementary, for the most part no more than ordinary arithmetic and algebra. There is some rudimentary and philosophically important employment of limits, but no use is made of integrals or differentials. Mathematical induction is rarely and inessentially employed in the text, but is more frequent and important in the apP'endix on set theory and Boolean algebra. • As far as logic is concerned, the book assumes a fair acquaintance with predicate logic and its techniques. The concepts of compactness and maximal consistency turn out to have important employment, which I have tried to keep self-contained, so that extensive knowledge of meta logical topics is not assumed. In a word, the book presupposes no more logical facility than is customary among working philosophers and graduate students, though it may call for unaccustomed vigor in its application.
