Logics for Propositional Determinacy and Independence

This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic D and Propositional Independence Logic I are recently developed logical systems, based on team semantics, that provide a framework for such reasoning tasks. We introduce two new logics LD and L I , based on Kripke semantics, and propose them as alternatives for D and I, respectively. We analyse the relative expressive powers of these four logics and discuss the way these systems relate to natural language. We argue that LD and L I naturally resolve a range of interpretational problems that arise in D and I. We also obtain sound and complete axiomatizations for LD and L I .