INCLUSION CRITERIA
An entry belongs in this division if and only if its semantics evaluates formulas on sets of assignments rather than on single assignments.
Required: At least one of the following:
- A satisfaction relation M, X ⊨ φ in which X is a set (team) of assignments
- An atom expressing a relation between variables not first-order expressible at a single assignment (dependence, independence, inclusion, exclusion, anonymity)
- Quantifiers evaluated by supplement or duplication functions on teams
Not sufficient: A Kripke semantics, in which a formula is evaluated at a world and the set of worlds is the model rather than the object of evaluation (that belongs in Modal). The test is where the formula is evaluated, not what the elements are: a modal logic whose formulas are evaluated at a *set* of worlds, with atoms constraining that set, is a team-semantic logic whose elements happen to be worlds, and belongs here cross-listed with Modal. A many-valued or degree semantics (Algebraic). Branching quantifiers presented only as an abbreviation in existential second-order logic, without a team-semantic evaluation.
Boundary: Modal and propositional dependence logics evaluate at a set of worlds or valuations and are placed here by that, not by the modality; they are cross-listed with Modal. Team semantics as a technique for characterizing expressive power is cross-listed with Metatheory/Model-Theory; the named logics built on it live here. Equivalence with existential second-order logic is a result about these logics, not the property that places them—an entry whose only claim is Σ¹₁-expressiveness belongs in Metatheory. The distinguishing move is the team, not the strength.