Juha Kontinen: Axiomatizing first-order consequences in dependence logic.

Dependence Logic, introduced by Jouko Väänänen in 2007, is a new logic incorporating the concept of dependence into first-order logic. The expressive power of dependence logic coincides with that of existential second-order logic In the past few years, dependence logic has grown into a new framework in which various notions of dependence and independence can be formalized. The high expressive power of dependence logic has a consequence that dependence logic in full generality cannot be axiomatized. However, first-order consequences of dependence logic sentences can be axiomatized. We give an explicit axiomatization and prove the respective Completeness Theorem. This is joint work with Jouko Väänänen.