: Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler, Jon Williamson
: Probabilistic Logics and Probabilistic Networks
: Springer-Verlag
: 9789400700086
: 1
: CHF 47.70
:
: Allgemeines, Lexika
: English
: 155
: Wasserzeichen/DRM
: PC/MAC/eReader/Tablet
: PDF
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.

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.
Preface7
Acknowledgements8
Contents9
Part I Probabilistic Logics12
1 Introduction13
1.1 The Fundamental Question of Probabilistic Logic13
1.2 The Potential of Probabilistic Logic14
1.3 Overview of the Book15
1.4 Philosophical and Historical Background17
1.5 Notation and Formal Setting19
2 Standard Probabilistic Semantics21
2.1 Background21
2.1.1 Kolmogorov Probabilities22
2.1.2 Interval-Valued Probabilities23
2.1.3 Imprecise Probabilities25
2.1.4 Convexity26
2.2 Representation28
2.3 Interpretation29
3 Probabilistic Argumentation31
3.1 Background32
3.2 Representation35
3.3 Interpretation36
3.3.1 Generalizing the Standard Semantics36
3.3.2 Premises from Unreliable Sources38
4 Evidential Probability42
4.1 Background42
4.1.1 Calculating Evidential Probability46
4.1.2 Extended Example: When Pigs Die49
4.2 Representation53
4.3 Interpretation53
4.3.1 First-order Evidential Probability54
4.3.2 Counterfactual Evidential Probability55
4.3.3 Second-Order Evidential Probability55
5 Statistical Inference58
5.1 Background58
5.1.1 Classical Statistics as Inference?58
5.1.2 Fiducial Probability61
5.1.3 Evidential Probability and Direct Inference64
5.2 Representation66
5.2.1 Fiducial Probability66
5.2.2 Evidential Probability and the Fiducial Argument67
5.3 Interpretation68
5.3.1 Fiducial Probability68
5.3.2 Evidential Probability69
6 Bayesian Statistical Inference71
6.1 Background71
6.2 Representation73
6.2.1 Infinitely Many Hypotheses74
6.2.2 Interval-Valued Priors and Posteriors76
6.3 Interpretation77
6.3.1 Interpretation of Probabilities77
6.3.2 Bayesian Confidence Intervals78
7 Objective Bayesian Epistemology80
7.1 Background80
7.1.1 Determining Objective Bayesian Degrees of Belief81
7.1.2 Constraints on Degrees of Belief82
7.1.3 Propositional Languages83
7.1.4 Predicate Languages84
7.1.5 Objective Bayesianism in Perspective86
7.2 Representation87
7.3 Interpretation87
Part II Probabilistic Networks90
8 Credal and Bayesian Networks91
8.1 Kinds of Probabilistic Network92
8.1.1 Extensions93
8.1.2 Extensions and Coordinates94
8.1.3 Parameterised Credal Networks96
8.2 Algorithms for Probabilistic Networks97
8.2.1 Requirements of the Probabilistic Logic Framework97
8.2.2 Compiling Probabilistic Networks98
8.2.3 The Hill-Climbing Algorithm for Credal Networks100
8.2.4 Complex Queries and Parameterised Credal Networks102
9 Networks for the Standard Semantics104
9.1 The Poverty of Standard Semantics104
9.2 Constructing a Credal Net105
9.3 Dilation and Independence109
10 Networks for Probabilistic Argumentation 111
10.1 Probabilistic Argumentation with Credal Sets111
10.2 Constructing and Applying the Credal Network112
11 Networks for Evidential Probability115
11.1 First-Order Evidential Probability115
11.2 Second-Order Evidential Probability117
11.3 Chaining Inferences120
12 Networks for Statistical Inference122
12.1 Functional Models and Networks122
12.1.1 Capturing the Fiducial Argument in a Network122
12.1.2 Aiding Fiducial Inference with Networks123
12.1.3 Trouble with Step-by-Step Fiducial Probability125
12.2 Evidential Probability and the Fiducial Argument126
12.2.1 First-Order EP and the Fiducial Argument126
12.2.2 Second-Order EP and the Fiducial Argument127
13 Networks for Bayesian Statistical Inference128
13.1 Credal Networks as Statistical Hypotheses128
13.1.1 Construction of the Credal Network129
13.1.2 Computational Advantages of Using the Credal Network130
13.2 Extending Statistical Inference with Credal Networks131
13.2.1 Interval-Valued Likelihoods132
13.2.2 Logically Complex Statements with Statistical Hypotheses134
14 Networks for Objective Bayesianism 135
14.1 Propositional Languages135
14.2 Predicate Languages137
15 Conclusion140
References141
Index152