Dependence Logic: Theory and ApplicationsSamson Abramsky, Juha Kontinen, Jouko Väänänen, Heribert Vollmer 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 uptodate 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

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Contents
2  
5  
Grelling on Dependence  33 
On Strongly FirstOrder Dependencies  53 
Games for Inclusion Logic and FixedPoint Logic  73 
Remarks on Compositionality  99 
Independence in Model Theory  109 
Dependency as Question Entailment  129 
Approximation Logics for Subclasses of Probabilistic Conditional Independence and Hierarchical Dependence on Incomplete Data  183 
ContextSpecific and Local Independence in Markovian Dependence Structures  219 
Arrows Theorem  235 
Introduction to SecretSharing  261 
Other editions  View all
Dependence Logic: Theory and Applications Samson Abramsky,Juha Kontinen,Jouko Väänänen,Heribert Vollmer No preview available  2016 
Common terms and phrases
access structure arity Arrow’s Theorem axiomatization Bayesian networks classical formulas classical logic closure operation complete random variables Computer Science conditional independence context corresponding database defined Definition denote dependence and independence dependence atoms domain entailment example existential expressive power extension finite set firstorder formula firstorder logic fixedpoint FOHDs forking fragment Gdepends graph group decision GSCI statements Itrap implication problem inclusion logic independence notion Inquisitive Semantics interpretation Kontinen Lemma linear logic with team matroid means modal logic modelchecking games multivalued dependencies negation node Player posGFP proof propositional logic quantifiers random variables rankings Rashomon rule safety games satisfies secondorder logic secretsharing sentence settled Shelah social choice social choice theory special probability models Springer strongly firstorder Suppose team semantics team X theory truth assignment truthconditional tuples twotuple relations Väänänen voters worlds