Inclusion with repetitions and Boolean constants -- implication problems revisited

Inclusion dependencies form one of the most widely used dependency classes. We extend existing results on the axiomatization and computational complexity of their implication problem to two extended variants. We present an alternative completeness proof for standard inclusion dependencies and extend it to inclusion dependencies with repetitions that can express equalities between attributes. The proof uses only two values, enabling us to work in the Boolean setting. Furthermore, we study inclusion dependencies with Boolean constants, provide a complete axiomatization and show that no such system is k-ary. Additionally, the decision problems for both extended versions remain PSPACE-complete. The extended inclusion dependencies examined are common in team semantics, which serves as the formal framework for the results.