Dependence Logic with Generalized Quantifiers: Axiomatizations
Engström, Fredrik, Juha Kontinen, Jouko Väänánen · arXiv (Cornell University) · 2013
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.