Dependence Logic

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This volume explores various aspects of dependence and independence logics, encompassing both logical and computational dimensions. It also highlights applications in fields like statistics, social choice theory, databases, and computer security. The chapters are authored by leading experts invited to contribute based on presentations from seminars at the Schloss Dagstuhl Leibniz Center for Informatics in Germany and an Academy Colloquium at the Royal Netherlands Academy of Arts and Sciences. Collectively, these contributions offer a contemporary overview of this emerging interdisciplinary field, appealing to logicians, mathematicians, statisticians, philosophers, and scientists. Key topics include a survey of propositional, modal, and first-order variants of dependence logic; new findings on the expressive power of various dependence logic forms with different logical connectives and generalized dependence atoms; links between inclusion logic and least-fixed point logic; an examination of dependencies in databases, focusing on implication issues related to statistical conditional independencies and multivalued dependencies; Markovian models for characterizing dependencies and causality in multivariate systems; applications of dependence logic in social choice theory; and an introduction to secret sharing theory, emphasizing its connections to dependence and independence logic.