Annals of Pure and Applied Logic 170 (9):975-992 (2019)

Authors
Jouko A Vaananen
University of Helsinki
Abstract
Directed acyclic graphs (DAGs) constitute a qualitative representation for conditional independence (CI) properties of a probability distribution. It is known that every CI statement implied by the topology of a DAG is witnessed over it under a graph-theoretic criterion of d-separation. Alternatively, all such implied CI statements are derivable from the local independencies encoded by a DAG using the so-called semi-graphoid axioms. We consider Labeled Directed Acyclic Graphs (LDAGs) modeling graphically scenarios exhibiting context-specific independence (CSI). Such CSI statements are modeled by labeled edges, where labels encode contexts in which the edge vanishes. We study the problem of identifying all independence statements implied by the structure and the labels of an LDAG. We show that this problem is coNP-hard for LDAGs and formulate a sound extension of the semi-graphoid axioms for the derivation of such implied independencies. Finally we connect our study to certain qualitative versions of independence ubiquitous in database theory and teams semantics.
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DOI 10.1016/j.apal.2019.04.004
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References found in this work BETA

Dependence and Independence.Erich Grädel & Jouko Väänänen - 2013 - Studia Logica 101 (2):399-410.
Axiomatizing First-Order Consequences in Dependence Logic.Juha Kontinen & Jouko Väänänen - 2013 - Annals of Pure and Applied Logic 164 (11):1101-1117.
Axiomatizing First-Order Consequences in Independence Logic.Miika Hannula - 2015 - Annals of Pure and Applied Logic 166 (1):61-91.
Independence Logic and Abstract Independence Relations.Gianluca Paolini - 2015 - Mathematical Logic Quarterly 61 (3):202-216.

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Citations of this work BETA

On Elementary Logics for Quantitative Dependencies.Miika Hannula, Minna Hirvonen & Juha Kontinen - forthcoming - Annals of Pure and Applied Logic:103104.

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