We develop a semantics for independence logic with respect to what we will call general models. We then introduce a simpler entailment semantics for the same logic, and we reduce the validity problem in the former to the validity problem in the latter. Then we build a proof system for independence logic and prove its soundness and completeness with respect to entailment semantics.
"General Models and Entailment Semantics for Independence Logic." Notre Dame J. Formal Logic 54 (2) 253 - 275, 2013. https://doi.org/10.1215/00294527-1960506