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Sentential Probability Logic
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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 Logic with a Probability Semantics by : Theodore Hailperin
Download or read book Logic with a Probability Semantics written by Theodore Hailperin and published by Rowman & Littlefield. This book was released on 2011 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Probability Logics by : Zoran Ognjanović
Download or read book Probability Logics written by Zoran Ognjanović and published by Springer. This book was released on 2016-10-24 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Probability Theory by : E. T. Jaynes
Download or read book Probability Theory written by E. T. Jaynes and published by Cambridge University Press. This book was released on 2003-04-10 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: Index.
Download or read book The Logic of Chance written by John Venn and published by . This book was released on 1888 with total page 550 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 Probability and the Logic of Rational Belief by : Henry Ely Kyburg
Download or read book Probability and the Logic of Rational Belief written by Henry Ely Kyburg and published by . This book was released on 1961 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Logic of Chance written by John Venn and published by . This book was released on 1866 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Logic of Conditionals by : E.W. Adams
Download or read book The Logic of Conditionals written by E.W. Adams and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of the four chapters in this book, the first two discuss (albeit in consider ably modified form) matters previously discussed in my papers 'On the Logic of Conditionals' [1] and 'Probability and the Logic of Conditionals' [2], while the last two present essentially new material. Chapter I is relatively informal and roughly parallels the first of the above papers in discussing the basic ideas of a probabilistic approach to the logic of the indicative conditional, according to which these constructions do not have truth values, but they do have probabilities (equal to conditional probabilities), and the appropriate criterion of soundness for inferences involving them is that it should not be possible for all premises of the inference to be probable while the conclusion is improbable. Applying this criterion is shown to have radically different consequences from the orthodox 'material conditional' theory, not only in application to the standard 'fallacies' of the material conditional, but to many forms (e. g. , Contraposition) which have hitherto been regarded as above suspi cion. Many more applications are considered in Chapter I, as well as certain related theoretical matters. The chief of these, which is the most important new topic treated in Chapter I (i. e.
Book Synopsis Probability Logic by : Peter Holger Krauss
Download or read book Probability Logic written by Peter Holger Krauss and published by . This book was released on 1966 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Logical Foundations of Probability by : Rudolf Carnap
Download or read book Logical Foundations of Probability written by Rudolf Carnap and published by . This book was released on 1962 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Logic, Probability and Science written by and published by BRILL. This book was released on 2022-02-22 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the contents: Charles MORGAN: Canonical models and probabilistic semantics. - Francois LEPAGE: A many-valued probabilistic logic. - Piers RAWLING: The exchange paradox, finite additivity, and the principle of dominance. - Susan VINEBERG: The logical status of conditionalization and its role in confirmation. - Deborah MAYO: Science, error statistics, and arguing from error. - Mark N. LANCE: The best is the enemy of the good: Bayesian epistemology as a case study in unhelpful idealization. - Robert B. GARDNER & Michael C. WOOTEN: An application of Bayes' theorem to population genetics. - Peter D. JOHNSON, Jr.: Another look at group selection."
Book Synopsis Probability Theory and Probability Logic by : Peter Roeper
Download or read book Probability Theory and Probability Logic written by Peter Roeper and published by University of Toronto Press. This book was released on 1999-01-01 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a survey of many technical results in probability theory and probability logic, this monograph by two widely respected scholars offers a valuable compendium of the principal aspects of the formal study of probability. Hugues Leblanc and Peter Roeper explore probability functions appropriate for propositional, quantificational, intuitionistic, and infinitary logic and investigate the connections among probability functions, semantics, and logical consequence. They offer a systematic justification of constraints for various types of probability functions, in particular, an exhaustive account of probability functions adequate for first-order quantificational logic. The relationship between absolute and relative probability functions is fully explored and the book offers a complete account of the representation of relative functions by absolute ones. The volume is designed to review familiar results, to place these results within a broad context, and to extend the discussions in new and interesting ways. Authoritative, articulate, and accessible, it will interest mathematicians and philosophers at both professional and post-graduate levels.
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 285 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 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 Hans Reichenbach by : Hans Reichenbach
Download or read book Hans Reichenbach written by Hans Reichenbach and published by Springer Science & Business Media. This book was released on 1978-12-31 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Subjective Probability by : Richard Jeffrey
Download or read book Subjective Probability written by Richard Jeffrey and published by Cambridge University Press. This book was released on 2004-04-12 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample Text
