TEAM
Logics whose semantics evaluates a formula not at a single assignment but at a set of them—a team. The shift is not to the truth values, not to an accessibility relation, not to the structural rules, and not to the typing judgment: it is a change in what a formula is evaluated at, and it is what makes dependence, independence, inclusion, and exclusion expressible as atoms rather than as second-order paraphrases.
The division is organized by the relation the atoms express. Dependence entries make functional determination primitive. Independence entries make informational independence primitive, including the branching-quantifier tradition that motivated the shift. Inclusion and exclusion entries take containment and disjointness of value-sets as primitive.
Every entry answers the collection's seven questions, and the Formalism slot carries the team semantics itself: what a team is, how the connectives split or preserve it, and how the quantifiers supplement or duplicate it.