Probabilistic Logics and Probabilistic Networks

1. Front Matter

   Pages i-xiii

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2. Probabilistic Logics

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 3-10

   3. Standard Probabilistic Semantics

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 11-20

   4. Probabilistic Argumentation

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 21-31

   5. Evidential Probability

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 33-48

   6. Statistical Inference

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 49-61

   7. Bayesian Statistical Inference

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 63-71

   8. Objective Bayesian Epistemology

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 73-82

3. Probabilistic Networks

   1. Front Matter

      Pages 83-83

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   2. Credal and Bayesian Networks

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 85-97

   3. Networks for the Standard Semantics

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 99-105

   4. Networks for Probabilistic Argumentation

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 107-110

   5. Networks for Evidential Probability

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 111-117

   6. Networks for Statistical Inference

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 119-124

   7. Networks for Bayesian Statistical Inference

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 125-131

   8. Networks for Objective Bayesianism

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 133-137

   9. Conclusion

      • Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson

      Pages 139-139

4. Back Matter

   Pages 141-155

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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.

• Bayesian networks
• Bayesian statistical inference
• Computational logic
• Computational methods
• Credal networks
• Evidential probability
• Objective Bayesian epistemology
• Probabilism
• Probabilistic argumentation
• Probabilistic logic
• Probabilistic semantics
• Probabilities
• Probability
• Probability theory

“The authors have a wide range of experience in this field and, with this book, they aim at the ambitious and meaningful goal of showing how several distinct approaches to probabilistic logic can be incorporated into a general framework. … It will be particularly appreciated by researchers who would like a unifying view of the several approaches to probabilistic logic.” (Renato Pelessoni, Mathematical Reviews, June, 2015)

"The authors of this book come from different academic backgrounds and disciplines (evidential probability [Wheeler, computer science]; probabilistic argumentation [Haenni, computer science]; objective Bayesianism [Williamson, philosophy]; and statistical inference [Romeijn, philosophy and psychology]). Their common interest is to investigate different logical and probabilistic inferential systems and to produce an unified view of inference in probabilistic logic. The group also has an eye toward computational feasibility, leading them to investigate applications of probabilistic networks to the inferential systems they try to unify. This book is the result of research began in 2005 as part of a program called Progic funded by the Leverhulme Trust. The project sponsored a series of excellent conferences centering on the problem of integrating logic and probability. While the focus of the book is probabilistic

and statistical inference, it could perfectly well serve as an introduction to the different inferential systems the authors consider. The book represents a valuable step towards a solution of the difficult and interesting problems which arise when trying to combine probability and logic."
Horacio Arlo-Costa, Carnegie Mellon University, Pittsburgh, U.S.A.


‘Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler and Jon Williamson make a heroic tour de force through these theories of probabilistic reasoning, with the aim of identifying a unifying overarching framework.’
Jan Sprenger, Tilburg Center for Logic and Philosophy of Science in Metascience, The Netherlands

Read the complete review: http://www.springerlink.com/content/pr7j017516052304/

• Inst. Informatik und, Angewandte Mathematik (IAM), Universität Bern, Bern, Switzerland

  Rolf Haenni

• , Faculty of Philosophy, University of Groningen, Groningen, Netherlands

  Jan-Willem Romeijn

• Fac. Ciencias e Tecnologia (FCT), Universidade Nova de Lisboa, Monte Caparica, Portugal

  Gregory Wheeler

• School of European Culture &, Languages, University of Kent, Canterbury, Kent, United Kingdom

  Jon Williamson

Rolf Haenni is professor at the Department of Engineering and Information Technology of the University of Applied Sciences of Berne (BFH-TI) in Biel, Switzerland. He holds a PhD degree in Computer Science from the University of Fribourg, for which he received the prize for the best thesis in 1996. Jan-Willem Romeijn is an assistant professor at the Philosophy Faculty of the University of Groningen. He obtained degrees cum laude in both physics and philosophy, worked as a financial mathematician and received his doctorate cum laude from the University of Groningen in 2005. Gregory Wheeler is Senior Research Scientist at the Centre for Artificial Intelligence at the New University of Lisbon. He received a joint PhD in Philosophy and Computer Science from the University of Rochester in 2002. Jon Williamson is Professor of Reasoning, Inference and Scientific Method at the University of Kent. He completed his PhD in Philosophy in 1998 and in 2007 was Times Higher Education UK Young Researcher of the Year.

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