  Since the introduction by Hodges, and refinement by V\"a\"an\"anen, team
semantic constructions have been used to generate expressively enriched logics
still conserving nice properties, such as compactness or decidability. In
contrast, these logics fail to be substitutional, limiting any algebraic
treatment, and rendering schematic uniform proof systems impossible. This
shortcoming can be attributed to the flatness principle, commonly adhered to
when generating team semantics. Investigating the formation of team semantics
from algebraic semantics, and disregarding the flatness principle, we present
the logic of teams, LT, a substitutional logic for which important
propositional team logics are axiomatisable as fragments. Starting from
classical propositional logic and Boolean algebras, we give semantics for LT by
considering the algebras that are powersets of Boolean algebras B, equipped
with internal (point-wise) and external (set-theoretic) connectives.
Furthermore, we present a well-motivated complete and sound labelled natural
deduction system for LT.
