Dependence Logic: Theory and Applications

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.
  

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