A finite axiomatization of conditional independence and inclusion dependencies

We formulate a finite axiomatization of the implication problem for inclusion and conditional independence atoms (dependencies) in the dependence logic context. The input of this problem is given by a finite set Σ {φ} consisting of conditional independence atoms and inclusion atoms, and the question to decide is whether the following logical consequence holds Σ φ. (1) Independence logic [12] and inclusion logic [6] are recent variants of dependence logic the semantics of which are defined over sets of assigments (teams) rather than a single assignment as in first-order logic.