  First-order logic is known to have limited expressive power over finite
structures. It enjoys in particular the locality property, which states that
first-order formulae cannot have a global view of a structure. This limitation
ensures on their low sequential computational complexity. We show that the
locality impacts as well on their distributed computational complexity. We use
first-order formulae to describe the properties of finite connected graphs,
which are the topology of communication networks, on which the first-order
formulae are also evaluated. We show that over bounded degree networks and
planar networks, first-order properties can be frugally evaluated, that is,
with only a bounded number of messages, of size logarithmic in the number of
nodes, sent over each link. Moreover, we show that the result carries over for
the extension of first-order logic with unary counting.
