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Dependence Logic

Theory and Applications

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  • © 2016

Overview

Editors:
  1. Samson Abramsky

    1. Department of Computer Science, University of Oxford, Oxford, United Kingdom

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  2. Juha Kontinen

    1. Department of Mathematics & Statistics, University of Helsinki, Helsinki, Finland

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  3. Jouko Väänänen

    1. Dept of Mathematics & Statistics, University of Helsinki, Helsinki, Finland

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  4. Heribert Vollmer

    1. Institut für Theoretische Informatik, Leibniz Universität Hannover, Hannover, Germany

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  • Covers a relatively new area of logic, introduced by Väänänen, that has seen rapid development
  • Dependence logic has applications in numerous, seemingly unrelated subjects, including causality, random variables in statistics, database theory, Mendelian genetics, and quantum physics
  • Will be of interest to a broad group of logicians, mathematicians, statisticians, philosophers, and scientists
  • Includes supplementary material: sn.pub/extras

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Introduction

    • Samson Abramsky, Juha Kontinen, Jouko Väänänen, Heribert Vollmer
    Pages 1-3

  3. Expressivity and Complexity of Dependence Logic

    • Arnaud Durand, Juha Kontinen, Heribert Vollmer
    Pages 5-32

  4. Grelling on Dependence

    • Jouko Väänänen
    Pages 33-52

  5. On Strongly First-Order Dependencies

    • Pietro Galliani
    Pages 53-71

  6. Games for Inclusion Logic and Fixed-Point Logic

    • Erich Grädel
    Pages 73-98

  7. Remarks on Compositionality

    • Wilfrid Hodges
    Pages 99-107

  8. Independence in Model Theory

    • Åsa Hirvonen
    Pages 109-128

  9. Dependency as Question Entailment

    • Ivano Ciardelli
    Pages 129-181

  10. Approximation Logics for Subclasses of Probabilistic Conditional Independence and Hierarchical Dependence on Incomplete Data

    • Sebastian Link
    Pages 183-217

  11. Context-Specific and Local Independence in Markovian Dependence Structures

    • Henrik Nyman, Johan Pensar, Jukka Corander
    Pages 219-234

  12. Dependence and Independence in Social Choice: Arrow’s Theorem

    • Eric Pacuit, Fan Yang
    Pages 235-260

  13. Introduction to Secret-Sharing

    • Andreas Blass
    Pages 261-276
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Keywords

About this book

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.



Editors and Affiliations

  • Department of Computer Science, University of Oxford, Oxford, United Kingdom

    Samson Abramsky

  • Department of Mathematics & Statistics, University of Helsinki, Helsinki, Finland

    Juha Kontinen

  • Dept of Mathematics & Statistics, University of Helsinki, Helsinki, Finland

    Jouko Väänänen

  • Institut für Theoretische Informatik, Leibniz Universität Hannover, Hannover, Germany

    Heribert Vollmer

About the editors

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

Bibliographic Information

  • Book Title: Dependence Logic

  • Book Subtitle: Theory and Applications

  • Editors: Samson Abramsky, Juha Kontinen, Jouko Väänänen, Heribert Vollmer

  • DOI: https://doi.org/10.1007/978-3-319-31803-5

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-31801-1Published: 06 July 2016

  • Softcover ISBN: 978-3-319-81123-9Published: 24 June 2018

  • eBook ISBN: 978-3-319-31803-5Published: 29 June 2016

  • Edition Number: 1

  • Number of Pages: XIV, 276

  • Number of Illustrations: 23 b/w illustrations

  • Topics: Mathematical Logic and Foundations, Mathematical Logic and Formal Languages, Logic

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