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E-raamat: Dependence Logic: Theory and Applications

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  • Ilmumisaeg: 29-Jun-2016
  • Kirjastus: Birkhauser Verlag AG
  • Keel: eng
  • ISBN-13: 9783319318035
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Dependence Logic: Theory and ApplicationsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 29-Jun-2016
  • Kirjastus: Birkhauser Verlag AG
  • Keel: eng
  • ISBN-13: 9783319318035
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In this volume, different aspects of logics for dependence and independence are discussed, including both the  logical and computational aspects of dependence logic, and also applications  in a number of areas, such as statistics, social choice theory, databases and computer security.  The contributing authors represent leading experts in this relatively new field, each of whom was invited to write a chapter based on talks given at seminars held at the Schloss Dagstuhl Leibniz Center for Informatics in Wadern, Germany (in February 2013 and June 2015) and an Academy Colloquium at the Royal Netherlands Academy of Arts and Sciences (March 2014).  Altogether, these chapters provide the most up-to-date look at this developing and highly interdisciplinary field and will be of interest to a broad group of logicians, mathematicians, statisticians, philosophers, and scientists. Topics covered include

  • a comprehensive survey of many propositional, modal, and first-order variants of dependence logic;
  • new results concerning expressive power of several variants of dependence logic with different sets of logical connectives and generalized dependence atoms;
  • connections between inclusion logic and the least-fixed point logic;
  • an overview of dependencies in databases by addressing the relationships between implication problems for fragments of statistical conditional independencies, embedded multivalued dependencies, and propositional logic;
  • various Markovian models used to characterize dependencies and causality among variables in multivariate systems;
  • applications of dependence logic in social choice theory; and
  • an introduction to the theory of secret sharing, pointing out connections to dependence and independence logic.

Contributors xiii
Introduction 1(4)
Samson Abramsky
Juha Kontinen
Jouko Vaananen
Heribert Vollmer
Expressivity and Complexity of Dependence Logic
5(28)
Arnaud Durand
Juha Kontinen
Heribert Vollmer
1 Introduction
5(1)
2 First-order Dependence Logic
6(11)
2.1 Team semantics
6(3)
2.2 Normal forms
9(1)
2.3 Expressive Power
10(3)
2.4 Refining the correspondence with εSO
13(2)
2.5 Satisfiability and Model Checking
15(2)
3 Propositional and Modal Dependence Logic
17(11)
3.1 Preliminaries
17(4)
3.2 Expressivity
21(3)
3.3 Complexity
24(3)
3.4 Propositional Logic
27(1)
4 Conclusion
28(5)
References
28(5)
Grelling on Dependence
33(20)
Jouko Vaananen
1 Introduction
33(2)
2 Dependence
35(5)
3 Interdependence and mutual dependence
40(1)
4 G-dependence
41(7)
5 G-dependence logic
48(3)
6 Conclusion
51(2)
References
51(2)
On Strongly First-Order Dependencies
53(20)
Pietro Galliani
1 Introduction
53(1)
2 Preliminaries
54(6)
3 On the Contradictory Negation
60(3)
4 Arity Hierarchies for Totality Atoms
63(2)
5 0-ary Dependencies: Escaping the Empty Team
65(1)
6 Unary Dependencies
66(3)
7 Conclusion
69(4)
References
70(3)
Games for Inclusion Logic and Fixed-Point Logic
73(26)
Erich Gradel
1 Introduction
73(2)
2 Safety games and traps
75(2)
3 Second-order reachability games
77(3)
4 Logics and Their Games
80(9)
4.1 First-order logic
80(1)
4.2 Least fixed-point logic
80(2)
4.3 The fragment of positive greatest fixed points
82(1)
4.4 Logics with team semantics
83(4)
4.5 Inclusion logic
87(2)
5 Interpretations
89(3)
6 Interpretability of game graphs
92(2)
7 Least fixed-point logic versus inclusion logic
94(5)
References
98(1)
Remarks on Compositionality
99(10)
Wilfrid Hodges
1 Compositionality in the background of dependence logic
99(2)
2 Compositional translation?
101(3)
3 The history of compositionality
104(5)
References
106(3)
Independence in Model Theory
109(20)
Asa Hirvonen
1 Introduction
109(1)
2 Notation and preliminaries
110(2)
3 Forking independence
112(2)
4 Pregeometries
114(1)
5 Ranks and independence
115(1)
6 Uniqueness
115(1)
7 Towards greater generality I: unstable classes
116(4)
7.1 Simple theories
117(2)
7.2 NIP theories
119(1)
7.3 Thorn-forking
119(1)
8 Towards greater generality II: non-elementary classes
120(6)
8.1 Finite diagrams or homogeneous model theory
120(3)
8.2 Excellent classes
123(1)
8.3 Abstract elementary classes
124(2)
9 Conclusion
126(3)
References
127(2)
Dependency as Question Entailment
129(54)
Ivano Ciardelli
1 Introduction
129(2)
2 Dependency is question entailment
131(12)
2.1 A motivating example
132(1)
2.2 Support semantics for classical logic
133(2)
2.3 Bringing questions into the picture
135(1)
2.4 Entailment
135(1)
2.5 Entailment in context
136(3)
2.6 Internalizing entailment
139(1)
2.7 Conditional dependencies
140(1)
2.8 Relation between questions or relation between variables?
141(1)
2.9 Summing up
142(1)
3 Propositional logic
143(10)
3.1 Support semantics for classical propositional logic
143(2)
3.2 Enriching propositional logic with questions
145(3)
3.3 Propositional dependencies
148(3)
3.4 Higher-order dependencies and the embedding problem
151(2)
4 Reasoning with questions and dependencies
153(11)
4.1 Properties of entailment
153(5)
4.2 Proof system
158(2)
4.3 Completeness
160(2)
4.4 Computational content of proofs involving questions
162(2)
4.5 Summing up
164(1)
5 Predicate logic
164(13)
5.1 What semantic setting?
164(2)
5.2 Quantification in support semantics
166(3)
5.3 A glance at the system
169(1)
5.4 First-order questions
170(1)
5.5 First-order dependencies
171(5)
5.6 Summing up
176(1)
6 Conclusion
177(6)
Appendix
178(1)
References
179(4)
Approximation Logics for Subclasses of Probabilistic Conditional Independence and Hierarchical Dependence on Incomplete Data
183(36)
Sebastian Link
1 Introduction
184(2)
2 Generalized Conditional Independence under Incomplete Data
186(4)
2.1 Complete Random Variables
186(1)
2.2 Conditional Independence under Complete Random Variables
187(3)
3 Axiomatizing GSCI Statements and Complete R.V.
190(7)
3.1 Sound Inference Rules
190(3)
3.2 The Independence Basis
193(1)
3.3 Completeness
194(2)
3.4 Special Probability Models
196(1)
4 Characterization by an S-3 Fragment
197(5)
4.1 Syntax and Semantics of S-3 logic
197(1)
4.2 The Propositional Fragment
198(1)
4.3 Special Truth Assignments
199(1)
4.4 Semantic Justification of Special Truth Assignments
200(1)
4.5 The Equivalence
201(1)
5 Full Hierarchical Dependencies and NOT NULL constraints
202(10)
5.1 Defining Hierarchical Dependencies under Incomplete Data
203(2)
5.2 Axiomatization
205(3)
5.3 Implication of FOHDs and NOT NULL Constraints in the World of Two-tuple Relations
208(1)
5.4 Functional and Hierarchical Dependencies
209(1)
5.5 Equivalence to the Propositional Fragment
210(2)
6 Related Work
212(2)
7 Conclusion
214(5)
References
214(5)
Context-Specific and Local Independence in Markovian Dependence Structures
219(16)
Henrik Nyman
Johan Pensar
Jukka Corander
1 Introduction
219(1)
2 Bayesian networks
220(7)
2.1 Bayesian networks with structured CPTs
223(3)
2.2 The role of CSI in model learning and probabilistic inference
226(1)
3 Markov networks
227(2)
4 Markov chains
229(2)
5 Discussion
231(4)
References
232(3)
Dependence and Independence in Social Choice: Arrow's Theorem
235(26)
Eric Pacuit
Fan Yang
1 Introduction
235(1)
2 The Social Choice Framework
236(2)
3 Dependence in Social Choice Theory
238(5)
4 Independence in Social Choice Theory
243(2)
5 Dependence and Independence Logic for Social Choice Theory
245(11)
5.1 The Logic
247(3)
5.2 Expressing Arrow's Conditions
250(4)
5.3 Arrow's Theorem
254(2)
6 Concluding Remarks
256(5)
References
258(3)
Introduction to Secret-Sharing
261
Andreas Blass
1 Basic Examples and Definitions
261(3)
2 Dependence and Independence
264(1)
3 Shamir's Scheme and Linear Schemes
265(1)
4 Matroids and Matroid-Related Schemes
266(4)
5 Examples
270(3)
6 Entropy and Inequalities
273
References
276
Samson Abramsky, Christopher Strachey Professor of Computing, Department of Computer Science, Oxford University, UK Juha Kontinen, Academy Research Fellow, Department of Mathematics and Statistics, Helsinki University, Finland Jouko Väänänen, Dean of the Faculty of Science and Professor, Department of Mathematics and Statistics, Helsinki University, Finland; Professor, University of Amsterdam, The Netherlands

Heribert Vollmer, Faculty of Electrical Engineering and Computer Science, Theoretical Computer Science Institute, University of Hannover, Germany
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