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Probabilistic Logics and Probabilistic Networks 2011 ed. [Kõva köide]

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  • Formaat: Hardback, 155 pages, kõrgus x laius: 235x155 mm, kaal: 930 g, XIII, 155 p., 1 Hardback
  • Sari: Synthese Library 350
  • Ilmumisaeg: 02-Dec-2010
  • Kirjastus: Springer
  • ISBN-10: 9400700075
  • ISBN-13: 9789400700079
Teised raamatud teemal:
Probabilistic Logics and Probabilistic Networks 2011 ed.Suurem pilt
  • Formaat: Hardback, 155 pages, kõrgus x laius: 235x155 mm, kaal: 930 g, XIII, 155 p., 1 Hardback
  • Sari: Synthese Library 350
  • Ilmumisaeg: 02-Dec-2010
  • Kirjastus: Springer
  • ISBN-10: 9400700075
  • ISBN-13: 9789400700079
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9789400700079.html
Märksõnad:
Probabilistic Logic and Probabilistic Networks presents a groundbreaking framework within which various approaches to probabilistic logic naturally fit. Additionally, the text shows how to develop computationally feasible methods to mesh with this framework.

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.

Arvustused

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/

Part I Probabilistic Logics
1 Introduction
3(8)
1.1 The Fundamental Question of Probabilistic Logic
3(1)
1.2 The Potential of Probabilistic Logic
4(1)
1.3 Overview of the Book
5(2)
1.4 Philosophical and Historical Background
7(2)
1.5 Notation and Formal Setting
9(2)
2 Standard Probabilistic Semantics
11(10)
2.1 Background
11(7)
2.1.1 Kolmogorov Probabilities
12(1)
2.1.2 Interval-Valued Probabilities
13(2)
2.1.3 Imprecise Probabilities
15(1)
2.1.4 Convexity
16(2)
2.2 Representation
18(1)
2.3 Interpretation
19(2)
3 Probabilistic Argumentation
21(12)
3.1 Background
22(3)
3.2 Representation
25(1)
3.3 Interpretation
26(7)
3.3.1 Generalizing the Standard Semantics
26(2)
3.3.2 Premises from Unreliable Sources
28(5)
4 Evidential Probability
33(16)
4.1 Background
33(11)
4.1.1 Calculating Evidential Probability
37(3)
4.1.2 Extended Example: When Pigs Die
40(4)
4.2 Representation
44(1)
4.3 Interpretation
44(5)
4.3.1 First-order Evidential Probability
45(1)
4.3.2 Counterfactual Evidential Probability
46(1)
4.3.3 Second-Order Evidential Probability
46(3)
5 Statistical Inference
49(14)
5.1 Background
49(8)
5.1.1 Classical Stistics as Inference?
49(3)
5.1.2 Fiducial Probability
52(3)
5.1.3 Evidential Probability and Direct Inference
55(2)
5.2 Representation
57(2)
5.2.1 Fiducial Probability
57(1)
5.2.2 Evidential Probability and the Fiducial Argument
58(1)
5.3 Interpretation
59(4)
5.3.1 Fiducial Probability
59(1)
5.3.2 Evidential Probability
60(3)
6 Bayesian Statistical Inference
63(10)
6.1 Background
63(2)
6.2 Representation
65(4)
6.2.1 Infinitely Many Hypotheses
66(2)
6.2.2 Interval-Valued Priors and Posteriors
68(1)
6.3 Interpretation
69(4)
6.3.1 Interpretation of Probabilities
69(1)
6.3.2 Bayesian Confidence Intervals
70(3)
7 Objective Bayesian Epistemology
73(12)
7.1 Background
73(7)
7.1.1 Determining Objective Bayesian Degrees of Belief
74(1)
7.1.2 Constraints on Degrees of Belief
75(1)
7.1.3 Propositional Languages
76(1)
7.1.4 Predicate Languages
77(2)
7.1.5 Objective Bayesianism in Perspective
79(1)
7.2 Representation
80(1)
7.3 Interpretation
80(5)
Part II Probabilistic Networks
8 Credal and Bayesian Networks
85(14)
8.1 Kinds of Probabilistic Network
86(5)
8.1.1 Extensions
87(1)
8.1.2 Extensions and Coordinates
88(2)
8.1.3 Parameterised Credal Networks
90(1)
8.2 Algorithms for Probabilistic Networks
91(8)
8.2.1 Requirements of the Probabilistic Logic Framework
91(1)
8.2.2 Compiling Probabilistic Networks
92(2)
8.2.3 The Hill-Climbing Algorithm for Credal Networks
94(2)
8.2.4 Complex Queries and Parameterised Credal Networks
96(3)
9 Networks for the Standard Semantics
99(8)
9.1 The Poverty of Standard Semantics
99(1)
9.2 Constructing a Credal Net
100(4)
9.3 Dilation and Independence
104(3)
10 Networks for Probabilistic Argumentation
107(4)
10.1 Probabilistic Argumentation with Credal Sets
107(1)
10.2 Constructing and Applying the Credal Network
108(3)
11 Networks for Evidential Probability
111(8)
11.1 First-Order Evidential Probability
111(2)
11.2 Second-Order Evidential Probability
113(3)
11.3 Chaining Inferences
116(3)
12 Networks for Statistical Inference
119(6)
12.1 Functional Models and Networks
119(4)
12.1.1 Capturing the Fiducial Argument in a Network
119(1)
12.1.2 Aiding Fiducial Inference with Networks
120(2)
12.1.3 Trouble with Step-by-Step Fiducial Probability
122(1)
12.2 Evidential Probability and the Fiducial Argument
123(2)
12.2.1 First-Order EP and the Fiducial Argument
123(1)
12.2.2 Second-Order EP and the Fiducial Argument
124(1)
13 Networks for Bayesian Statistical Inference
125(8)
13.1 Credal Networks as Statistical Hypotheses
125(3)
13.1.1 Construction of the Credal Network
126(1)
13.1.2 Computational Advantages of Using the Credal Network
127(1)
13.2 Extending Statistical Inference with Credal Networks
128(5)
13.2.1 Interval-Valued Likelihoods
129(2)
13.2.2 Logically Complex Statements with Statistical Hypotheses
131(2)
14 Networks for Objective Bayesianism
133(6)
14.1 Propositional Languages
133(2)
14.2 Predicate Languages
135(4)
15 Conclusion
139(2)
References 141(12)
Index 153
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.