Finitary closure operators

Is there a reasonably general dimension theory for finitary closure operators? It seems reasonable to restrict to the finite case first. Two cases with a dimension theory are known: How about greedoids? Matroids and antimatroids are interval greedoids. Can all interval greedoids be described in terms of a closure operator?
 * matroids have an excellent dimension theory
 * antimatroids have a satisfactory dimension theory.