Negation and Partial Axiomatizations of Dependence and Independence Logic Revisited

摘要

In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the natural deduction systems of the logics given in. We give a characterization 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.