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We prove two completeness results, one for the extension of dependence logicby a monotone generalized quantifier Q with weak interpretation, weak in themeaning that the interpretation of Q varies with the structures. The secondresult considers the extension of dependence logic where Q is interpreted as"there exists uncountable many." Both of the axiomatizations are shown to besound and complete for FO(Q) consequences.

Dependence Logic with Generalized Quantifiers: Axiomatizations