Inclusion and Exclusion Dependencies in Team Semantics: On Some Logics of Imperfect Information

Abstract

We introduce some new logics of imperfect information by adding atomic formulas corresponding to inclusion and exclusion dependencies to the language of first order logic. The properties of these logics and their relationships with other logics of imperfect information are then studied. Furthermore, a game theoretic semantics for these logics is developed. As a corollary of these results, we characterize the expressive power of independence logic, thus answering an open problem posed in (Gr\"adel and V\"a\"an\"anen, 2010).