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Dependence Logic with Generalized Quantifiers: Axiomatizations (1304.0611v1)
Published 2 Apr 2013 in math.LO and cs.LO
Abstract: We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result considers the extension of dependence logic where Q is interpreted as "there exists uncountable many." Both of the axiomatizations are shown to be sound and complete for FO(Q) consequences.