Annals of Pure and Applied Logic 170 (9):1128-1149 (2019)

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Abstract
In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the systems of natural deduction of the logics given in [22] and [11]. We prove a characterization theorem for negatable formulas in independence logic and negatable sentences in dependence logic, and identify an interesting class of formulas that are negatable in independence logic. Dependence and independence atoms, first-order formulas belong to this class. We also demonstrate our extended system of independence logic by giving explicit derivations for Armstrong's Axioms and the Geiger-Paz-Pearl axioms of dependence and independence atoms.
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DOI 10.1016/j.apal.2019.04.010
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Axiomatizations of Team Logics.Martin Lück - 2018 - Annals of Pure and Applied Logic 169 (9):928-969.
Axiomatizing First Order Consequences in Inclusion Logic.Fan Yang - forthcoming - Mathematical Logic Quarterly.

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