  This article provides an algebraic study of intermediate inquisitive and
dependence logics. While these logics are usually investigated using team
semantics, here we introduce an alternative algebraic semantics and we prove it
is complete for all intermediate inquisitive and dependence logics. To this
end, we define inquisitive and dependence algebras and we investigate their
model-theoretic properties. We show they are elementary structures axiomatised
by Horn sentences and we use our completeness result to state a version of
algebraisability for inquisitive and dependence logics. We then focus on
finite, core-generated, well-connected inquisitive and dependence algebras: we
show they witness the validity of formulas true in inquisitive algebras, and of
formulas true in well-connected dependence algebras. Finally, we obtain
Representation Theorems for finite, core-generated, well-connected, inquisitive
and dependence algebras and we prove some results connecting team and algebraic
semantics.
