Abstract: Team logics are extensions of first-order logic that allow reasoning about interdependencies between assignments in a natural way. This increases the expressive power at the cost of high complexity.

In the first part of the talk, we look at team logics as fragments of existential second-order logics (ESO). There are prior classification results, for example that dependence logic is equivalent to the downward closed fragment of ESO, and independence logic is equivalent to ESO. We provide a general strategy to design and classify team logics that correspond to semantic fragments of ESO, including a classification of convex ESO and a novel classification of union closed ESO.

In the second part, we look at guarded team logics. Guarded logics are known for their robust tractability, which motivates the analysis of guarded variants of these logics. We provide a hierarchy of expressiveness for guarded variants of established team logics and introduce a novel class of team logics called "hybrid team logics" that combines expressive power with desirable algorithmic properties.