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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: Theodore Hailperin
Publisher: Rowman & Littlefield
ISBN: 1611460107
Category : Mathematics
Languages : en
Pages : 124
Get Book Here
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: Fabrizio Riguzzi
Publisher: CRC Press
ISBN: 1000923215
Category : Computers
Languages : en
Pages : 548
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Book Description
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. This book 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. This 2nd edition aims at reporting the most exciting novelties in the field since the publication of the 1st edition. The semantics for hybrid programs with function symbols was placed on a sound footing. Probabilistic Answer Set Programming gained a lot of interest together with the studies on the complexity of inference. Algorithms for solving the MPE and MAP tasks are now available. Inference for hybrid programs has changed dramatically with the introduction of Weighted Model Integration. With respect to learning, the first approaches for neuro-symbolic integration have appeared together with algorithms for learning the structure for hybrid programs. Moreover, given the cost of learning PLPs, various works proposed language restrictions to speed up learning and improve its scaling.
Author: Rolf Haenni
Publisher: Springer Science & Business Media
ISBN: 9400700083
Category : Science
Languages : en
Pages : 154
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Book Description
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: 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: Zoran Ognjanović
Publisher: Springer Nature
ISBN: 3030529541
Category : Computers
Languages : en
Pages : 245
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Book Description
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.
Author: Luc De Raedt
Publisher: Springer
ISBN: 354078652X
Category : Computers
Languages : en
Pages : 348
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Book Description
This book provides an introduction to probabilistic inductive logic programming. It places emphasis on the methods based on logic programming principles and covers formalisms and systems, implementations and applications, as well as theory.
Author: Gilles Barthe
Publisher: Cambridge University Press
ISBN: 110848851X
Category : Computers
Languages : en
Pages : 583
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Book Description
This book provides an overview of the theoretical underpinnings of modern probabilistic programming and presents applications in e.g., machine learning, security, and approximate computing. Comprehensive survey chapters make the material accessible to graduate students and non-experts. This title is also available as Open Access on Cambridge Core.
Author: Ivano Ciardelli
Publisher: Oxford University Press
ISBN: 019881478X
Category : Language Arts & Disciplines
Languages : en
Pages : 232
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Book Description
This is an open access title available under the terms of a CC BY-NC-ND 4.0 International licence. It is free to read at Oxford Scholarship Online and offered as a free PDF download from OUP and selected open access locations. This book presents a new logical framework to capture the meaning of sentences in conversation. The traditional approach equates meaning with truth-conditions: to know the meaning of a sentence is to know under which circumstances it is true. The reason for this is that linguistic and philosophical investigations are usually carried out in a logical framework that was originally designed to characterize valid argumentation. However, argumentation is neither the sole, nor the primary function of language. One task that language more widely and ordinarily fulfils is to enable the exchange of information between conversational participants. In the framework outlined in this volume, inquisitive semantics, information exchange is seen as a process of raising and resolving issues. Inquisitive semantics provides a new formal notion of meaning, which makes it possible to model various concepts that are crucial for the analysis of linguistic information exchange in a more refined and more principled way than has been possible in previous frameworks. Importantly, it also allows an integrated treatment of statements and questions. The first part of the book presents the framework in detail, while the second demonstrates its benefits in the semantic analysis of questions, coordination, modals, conditionals, and intonation. The book will be of interest to researchers and students from advanced undergraduate level upwards in the fields of semantics, pragmatics, philosophy of language, and logic.
Author: Guy Van den Broeck
Publisher: MIT Press
ISBN: 0262542595
Category : Computers
Languages : en
Pages : 455
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Book Description
Recent advances in the area of lifted inference, which exploits the structure inherent in relational probabilistic models. Statistical relational AI (StaRAI) studies the integration of reasoning under uncertainty with reasoning about individuals and relations. The representations used are often called relational probabilistic models. Lifted inference is about how to exploit the structure inherent in relational probabilistic models, either in the way they are expressed or by extracting structure from observations. This book covers recent significant advances in the area of lifted inference, providing a unifying introduction to this very active field. After providing necessary background on probabilistic graphical models, relational probabilistic models, and learning inside these models, the book turns to lifted inference, first covering exact inference and then approximate inference. In addition, the book considers the theory of liftability and acting in relational domains, which allows the connection of learning and reasoning in relational domains.
Author: Peter Roeper
Publisher: University of Toronto Press
ISBN: 9780802008077
Category : Philosophy
Languages : en
Pages : 268
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Book Description
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.
