  We introduce a new family of temporal logics designed to finely balance the
trade-off between expressivity and complexity. Their key feature is the
possibility of defining operators of a new kind that we call transformation
operators. Some of them subsume existing temporal operators, while others are
entirely novel. Of particular interest are transformation operators based on
semigroups. They enable logics to harness the richness of semigroup theory, and
we show them to yield logics capable of creating hierarchies of increasing
expressivity and complexity which are non-trivial to characterise in existing
logics. The result is a genuinely novel and yet unexplored landscape of
temporal logics, each of them with the potential of matching the trade-off
between expressivity and complexity required by specific applications.
