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  1. Dependence and Independence.Erich Grädel & Jouko Väänänen - 2013 - Studia Logica 101 (2):399-410.
    We introduce an atomic formula ${\vec{y} \bot_{\vec{x}}\vec{z}}$ intuitively saying that the variables ${\vec{y}}$ are independent from the variables ${\vec{z}}$ if the variables ${\vec{x}}$ are kept constant. We contrast this with dependence logic ${\mathcal{D}}$ based on the atomic formula = ${(\vec{x}, \vec{y})}$ , actually equivalent to ${\vec{y} \bot_{\vec{x}}\vec{y}}$ , saying that the variables ${\vec{y}}$ are totally determined by the variables ${\vec{x}}$ . We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. (...)
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  • Inclusion and exclusion dependencies in team semantics—on some logics of imperfect information.Pietro Galliani - 2012 - Annals of Pure and Applied Logic 163 (1):68-84.
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  • Axiomatizing first-order consequences in dependence logic.Juha Kontinen & Jouko Väänänen - 2013 - Annals of Pure and Applied Logic 164 (11):1101-1117.
    Dependence logic, introduced in Väänänen [11], cannot be axiomatized. However, first-order consequences of dependence logic sentences can be axiomatized, and this is what we shall do in this paper. We give an explicit axiomatization and prove the respective Completeness Theorem.
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  • Axiomatizing first-order consequences in independence logic.Miika Hannula - 2015 - Annals of Pure and Applied Logic 166 (1):61-91.
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  • On the conditional independence implication problem: A lattice-theoretic approach.Mathias Niepert, Marc Gyssens, Bassem Sayrafi & Dirk Van Gucht - 2013 - Artificial Intelligence 202:29-51.
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  • Dependence logic in pregeometries and ω-stable theories.Gianluca Paolini & Jouko Väänänen - 2016 - Journal of Symbolic Logic 81 (1):32-55.
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  • Independence logic and abstract independence relations.Gianluca Paolini - 2015 - Mathematical Logic Quarterly 61 (3):202-216.
    We continue the work on the relations between independence logic and the model-theoretic analysis of independence, generalizing the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a model-theoretic interpretation of the independence atom and characterize under which conditions we can prove a completeness result with respect to the deductive system that axiomatizes independence in team semantics and statistics.
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  • Knowledge representation and inference in similarity networks and Bayesian multinets.Dan Geiger & David Heckerman - 1996 - Artificial Intelligence 82 (1-2):45-74.
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  • Sound approximate reasoning about saturated conditional probabilistic independence under controlled uncertainty.Sebastian Link - 2013 - Journal of Applied Logic 11 (3):309-327.
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