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Author : Octav Onicescu
Publisher :
ISBN 13 :
Total Pages : 196 pages
Book Rating : 4.3/5 (91 download)
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:
Author : T. Hailperin
Publisher : Elsevier
ISBN 13 : 9780080880051
Total Pages : 427 pages
Book Rating : 4.8/5 (8 download)
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.
Author : Demetrios A. Kappos
Publisher : Academic Press
ISBN 13 : 1483218503
Total Pages : 280 pages
Book Rating : 4.4/5 (832 download)
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.
Author : A.M. Yaglom
Publisher : Springer Science & Business Media
ISBN 13 : 9789027715227
Total Pages : 454 pages
Book Rating : 4.7/5 (152 download)
Download or read book Probability and Information written by A.M. Yaglom and published by Springer Science & Business Media. This book was released on 1983-11-30 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Louis Narens
Publisher : World Scientific
ISBN 13 : 9812708014
Total Pages : 230 pages
Book Rating : 4.8/5 (127 download)
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.
Author :
Publisher :
ISBN 13 : 9814474932
Total Pages : pages
Book Rating : 4.8/5 (144 download)
Download or read book Theories of Probability written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Applebaum
Publisher : Cambridge University Press
ISBN 13 : 9780521555289
Total Pages : 234 pages
Book Rating : 4.5/5 (552 download)
Download or read book Probability and Information written by David Applebaum and published by Cambridge University Press. This book was released on 1996-07-13 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This elementary introduction to probability theory and information theory is suitable as a textbook for beginning students in mathematics, statistics or computer science who have some knowledge of basic calculus. It provides a clear and systematic foundation to the subject; the concept of probability is given particular attention via a highly simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics dealt with include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information. Many examples and exercises are included that illustrate how the theory can be applied, for example to information technology. Detailed solutions to most exercises are available electronically from the Cambridge WWW server.
Author :
Publisher : American Mathematical Soc.
ISBN 13 : 9780821814574
Total Pages : 312 pages
Book Rating : 4.8/5 (145 download)
Download or read book Twenty-Four Papers on Statistics and Probability written by and published by American Mathematical Soc.. This book was released on with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Louis Narens
Publisher : World Scientific
ISBN 13 : 9812770070
Total Pages : 230 pages
Book Rating : 4.8/5 (127 download)
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.
Author : Giulianella Coletti
Publisher : Springer Science & Business Media
ISBN 13 : 9401004749
Total Pages : 291 pages
Book Rating : 4.4/5 (1 download)
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.
Author : Philip Calabrese
Publisher :
ISBN 13 : 9781848902589
Total Pages : 286 pages
Book Rating : 4.9/5 (25 download)
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
Author : D.A. Vladimirov
Publisher : Springer Science & Business Media
ISBN 13 : 940170936X
Total Pages : 614 pages
Book Rating : 4.4/5 (17 download)
Download or read book Boolean Algebras in Analysis written by D.A. Vladimirov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boolean Algebras in Analysis consists of two parts. The first concerns the general theory at the beginner's level. Presenting classical theorems, the book describes the topologies and uniform structures of Boolean algebras, the basics of complete Boolean algebras and their continuous homomorphisms, as well as lifting theory. The first part also includes an introductory chapter describing the elementary to the theory. The second part deals at a graduate level with the metric theory of Boolean algebras at a graduate level. The covered topics include measure algebras, their sub algebras, and groups of automorphisms. Ample room is allotted to the new classification theorems abstracting the celebrated counterparts by D.Maharam, A.H. Kolmogorov, and V.A.Rokhlin. Boolean Algebras in Analysis is an exceptional definitive source on Boolean algebra as applied to functional analysis and probability. It is intended for all who are interested in new and powerful tools for hard and soft mathematical analysis.
Author : Ivan Kramosil
Publisher : Springer Science & Business Media
ISBN 13 : 9780306467028
Total Pages : 236 pages
Book Rating : 4.4/5 (67 download)
Download or read book Probabilistic Analysis of Belief Functions written by Ivan Kramosil and published by Springer Science & Business Media. This book was released on 2001-12-31 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspired by the eternal beauty and truth of the laws governing the run of stars on heavens over his head, and spurred by the idea to catch, perhaps for the smallest fraction of the shortest instant, the Eternity itself, man created such masterpieces of human intellect like the Platon's world of ideas manifesting eternal truths, like the Euclidean geometry, or like the Newtonian celestial me chanics. However, turning his look to the sub-lunar world of our everyday efforts, troubles, sorrows and, from time to time but very, very seldom, also our successes, he saw nothing else than a world full of uncertainty and tem porariness. One remedy or rather consolation was that of the deep and sage resignation offered by Socrates: I know, that I know nothing. But, happy or unhappy enough, the temptation to see and to touch at least a very small por tion of eternal truth also under these circumstances and behind phenomena charged by uncertainty was too strong. Probability theory in its most sim ple elementary setting entered the scene. It happened in the same, 17th and 18th centuries, when celestial mechanics with its classical Platonist paradigma achieved its greatest triumphs. The origins of probability theory were inspired by games of chance like roulettes, lotteries, dices, urn schemata, etc. and probability values were simply defined by the ratio of successful or winning results relative to the total number of possible outcomes.
Author : Hajnal Andréka
Publisher : Springer Science & Business Media
ISBN 13 : 3642350259
Total Pages : 457 pages
Book Rating : 4.6/5 (423 download)
Download or read book Cylindric-like Algebras and Algebraic Logic written by Hajnal Andréka and published by Springer Science & Business Media. This book was released on 2014-01-27 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways: as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.
Author : Emmanuel Haven
Publisher : Frontiers Media SA
ISBN 13 : 2889631508
Total Pages : 164 pages
Book Rating : 4.8/5 (896 download)
Download or read book Applications of Quantum Mechanical Techniques to Areas Outside of Quantum Mechanics. 2nd Edition written by Emmanuel Haven and published by Frontiers Media SA. This book was released on 2019-11-14 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with applications of quantum mechanical techniques to areas outside of quantum mechanics, so-called quantum-like modeling. Research in this area has grown over the last 15 years. But even already more than 50 years ago, the interaction between Physics Nobelist Pauli and the psychologist Carl Jung in the 1950’s on seeking to find analogous uses of the complementarity principle from quantum mechanics in psychology needs noting. This book does NOT want to advance that society is quantum mechanical! The macroscopic world is manifestly not quantum mechanical. But this rules not out that one can use concepts and the mathematical apparatus from quantum physics in a macroscopic environment. A mainstay ingredient of quantum mechanics, is ‘quantum probability’ and this tool has been proven to be useful in the mathematical modelling of decision making. In the most basic experiment of quantum physics, the double slit experiment, it is known (from the works of A. Khrennikov) that the law of total probability is violated. It is now well documented that several decision making paradoxes in psychology and economics (such as the Ellsberg paradox) do exhibit this violation of the law of total probability. When data is collected with experiments which test ‘non-rational’ decision making behaviour, one can observe that such data often exhibits a complex non-commutative structure, which may be even more complex than if one considers the structure allied to the basic two slit experiment. The community exploring quantum-like models has tried to address how quantum probability can help in better explaining those paradoxes. Research has now been published in very high standing journals on resolving some of the paradoxes with the mathematics of quantum physics. The aim of this book is to collect the contributions of world’s leading experts in quantum like modeling in decision making, psychology, cognition, economics, and finance.
Author : Ehtibar Dzhafarov
Publisher : World Scientific
ISBN 13 : 9814730629
Total Pages : 480 pages
Book Rating : 4.8/5 (147 download)
Download or read book Contextuality from Quantum Physics to Psychology written by Ehtibar Dzhafarov and published by World Scientific. This book was released on 2015-11-30 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explores the variety of meanings of contextuality across different disciplines, with the emphasis on quantum physics and on psychology. Contents:Conversations on Contextuality (Ehtibar N Dzhafarov & Janne V Kujala)Contextual Semantics (Samson Abransky)From Coupling to Copula (Hans Colonius)Einstein, Bohm, and Leggett-Garg (Guido Bacciagaluppi)It is the Theory Which Decides What We Can Observe (Thomas Filk)Reality, Contextuality, and Probability in Quantum Theory and Beyond (Arkady Plotnitsky)Contextual Emergence (Harald Atmanspacher)Contextuality in Physics and Quantum Cognition (J Acacio de Barros & Gary Oas)End-Directedness and Context in Nonliving Dissipative Systems (James A Dixon, Dilip Kondepudi, Bruce A Kay & Tehran J Davis)Foregrounding the Background (J Scott Jordan, Jiuyang Bai, Vincent Cialdella & Daniel Schloesser)Symmetry-Breaking in Multiagent Coordination (Michael J Richardson & Rachel W Kallen)Probabilistic Contextuality (Janne V Kujala & Ehtibar N Dzhafarov)Quantum Thinking and Counterfactual Reasoning (Louis Narens)Quantum Theory, Active Information and the Mind-Matter Problem (Paavo Pylkkänen)Principles Defining Quantum Mechanics (Gary Oas & J Acacio de Barros)Our (Represented) World: A Quantum-Like Object (Ariane Lambert-Mogiliansky & Francois Dubois)Why Would You Want to Borrow from My Discipline? (Emmanuel Haven)Quantum Information Biology (Masanari Asano, Irina Basieva, Andrei Khrennikov, Masanori Ohya, Yoshiharu Tanaka & Ichiro Yamato)Similarity Judgments: From Classical to Complex Vector Psychological Spaces (Albert Barque Duran, Emmanuel M Pothos, James M Yearsley, James A Hampton, Jerome R Busemeyer & Jennifer S Trueblood)A Quantum Bayes Net Approach to Causal Reasoning (Jennifer S Trueblood, Percy K Mistry & Emmanuel M Pothos) Readership: Researchers in quantum physics, mathematical modelling and cognitive science. Key Features:It is historically the first book dedicated entirely to contextualityIt is interdisciplinary, involving quantum physicists, computer scientists, mathematicians, analytic philosophers, economists, and psychologistsIts chapters are written by leading specialists in these various fieldsKeywords:Contextuality;Quantum Physics;Psychology
Author : Louis Narens
Publisher : World Scientific
ISBN 13 : 9814630438
Total Pages : 208 pages
Book Rating : 4.8/5 (146 download)
Download or read book Probabilistic Lattices written by Louis Narens and published by World Scientific. This book was released on 2014-12-30 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many books on lattice theory in the field, but none interfaces with the foundations of probability. This book does. It also develops new probability theories with rigorous foundations for decision theory and applies them to specific well-known problematic examples. There is only one other book that attempts this. It uses quantum probability theory from physics. The new probability theories developed in this book are different; they are not borrowed from physics but are explicitly designed for decision theory. Contents:IntroductionBasic Lattice TheoryPseudo Complemented Distributive LatticesProbability and CoherenceRationality, Heuristics, and Human Judgments of ProbabilityOrthomodular Modeling of Psychological Paradigms Readership: Researchers in probability theory, logic and mathematical psychology. Key Features:Systematic, foundational development of probability theories based on Boolean and non-Boolean algebrasNew theoretical foundations for theories of belief that emphasize the logical structure of event spacesNew methods for modeling the Kahnemann and Tversky heuristics and other psychological paradigms based on intuitionistic logic and a generalization of quantum logicKeywords:Probability on Lattices;Decision Theory;Intuitionistic Logic;Lattice Theory
