  We define and study "semimatroids", a class of objects which abstracts the
dependence properties of an affine hyperplane arrangement. We show that
geometric semilattices are precisely the posets of flats of semimatroids. We
define and investigate the Tutte polynomial of a semimatroid. We prove that it
is the universal Tutte-Grothendieck invariant for semimatroids, and we give a
combinatorial interpretation for its non-negative coefficients.
