Probability Logics
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Probability Logics
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Author : Zoran Ognjanović
language : en
Publisher: Springer
Release Date : 2016-10-24
Probability Logics written by Zoran Ognjanović and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-24 with Mathematics categories.
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.
Probabilistic Logics And Probabilistic Networks
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Author : Rolf Haenni
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-19
Probabilistic Logics And Probabilistic Networks written by Rolf Haenni and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-19 with Science categories.
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.
Probability Theory And Probability Logic
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Author : Peter Roeper
language : en
Publisher: University of Toronto Press
Release Date : 1999-01-01
Probability Theory And Probability Logic written by Peter Roeper and has been published by University of Toronto Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Philosophy categories.
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.
Probability Theory
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Author : E. T. Jaynes
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-10
Probability Theory written by E. T. Jaynes and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-10 with Mathematics categories.
Index.
Sentential Probability Logic
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Author : Theodore Hailperin
language : en
Publisher: Lehigh University Press
Release Date : 1996
Sentential Probability Logic written by Theodore Hailperin and has been published by Lehigh University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
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.
Probabilistic Extensions Of Various Logical Systems
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Author : Zoran Ognjanović
language : en
Publisher: Springer Nature
Release Date : 2020-07-17
Probabilistic Extensions Of Various Logical Systems written by Zoran Ognjanović and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-17 with Computers categories.
The contributions in this book survey results on combinations of probabilistic and various other classical, temporal and justification logical systems. Formal languages of these logics are extended with probabilistic operators. The aim is to provide a systematic overview and an accessible presentation of mathematical techniques used to obtain results on formalization, completeness, compactness and decidability. The book will be of value to researchers in logic and it can be used as a supplementary text in graduate courses on non-classical logics.
Logic With A Probability Semantics
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Author : Theodore Hailperin
language : en
Publisher: Rowman & Littlefield
Release Date : 2011
Logic With A Probability Semantics written by Theodore Hailperin and has been published by Rowman & Littlefield this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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
Representing And Reasoning With Probabilistic Knowledge
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Author : Fahiem Bacchus
language : en
Publisher: Cambridge, Mass. : MIT Press
Release Date : 1990
Representing And Reasoning With Probabilistic Knowledge written by Fahiem Bacchus and has been published by Cambridge, Mass. : MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Computers categories.
Probabilistic information has many uses in an intelligent system. This book explores logical formalisms for representing and reasoning with probabilistic information that will be of particular value to researchers in nonmonotonic reasoning, applications of probabilities, and knowledge representation. It demonstrates that probabilities are not limited to particular applications, like expert systems; they have an important role to play in the formal design and specification of intelligent systems in general. Fahiem Bacchus focuses on two distinct notions of probabilities: one propositional, involving degrees of belief, the other proportional, involving statistics. He constructs distinct logics with different semantics for each type of probability that are a significant advance in the formal tools available for representing and reasoning with probabilities. These logics can represent an extensive variety of qualitative assertions, eliminating requirements for exact point-valued probabilities, and they can represent firstshy;order logical information. The logics also have proof theories which give a formal specification for a class of reasoning that subsumes and integrates most of the probabilistic reasoning schemes so far developed in AI. Using the new logical tools to connect statistical with propositional probability, Bacchus also proposes a system of direct inference in which degrees of belief can be inferred from statistical knowledge and demonstrates how this mechanism can be applied to yield a powerful and intuitively satisfying system of defeasible or default reasoning. Fahiem Bacchus is Assistant Professor of Computer Science at the University of Waterloo, Ontario. Contents: Introduction. Propositional Probabilities. Statistical Probabilities. Combining Statistical and Propositional Probabilities Default Inferences from Statistical Knowledge.
Foundations Of Probabilistic Logic Programming
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Author : Fabrizio Riguzzi
language : en
Publisher: River Publishers
Release Date : 2018-09-01
Foundations Of Probabilistic Logic Programming written by Fabrizio Riguzzi and has been published by River Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-01 with Computers categories.
Probabilistic Logic Programming extends Logic Programming by enabling the representation of uncertain information. Probabilistic Logic Programming is at the intersection of two wider research fields: the integration of logic and probability and Probabilistic Programming. Logic enables the representation of complex relations among entities while probability theory is useful for model uncertainty over attributes and relations. Combining the two is a very active field of study. Probabilistic Programming extends programming languages with probabilistic primitives that can be used to write complex probabilistic models. Algorithms for the inference and learning tasks are then provided automatically by the system. Probabilistic Logic programming is at the same time a logic language, with its knowledge representation capabilities, and a Turing complete language, with its computation capabilities, thus providing the best of both worlds. Since its birth, the field of Probabilistic Logic Programming has seen a steady increase of activity, with many proposals for languages and algorithms for inference and learning. Foundations of Probabilistic Logic Programming aims at providing an overview of the field with a special emphasis on languages under the Distribution Semantics, one of the most influential approaches. The book presents the main ideas for semantics, inference, and learning and highlights connections between the methods. Many examples of the book include a link to a page of the web application http://cplint.eu where the code can be run online.
Contributions To The Model Theory Of Probability Logics
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Author : Sergio Fajardo
language : en
Publisher:
Release Date : 1984
Contributions To The Model Theory Of Probability Logics written by Sergio Fajardo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Probabilities categories.
