Abstract
A dependence space is an ordered pair consisting of a nonempty finite set and a congruence on its boolean lattice, and is viewed as a general model to deal with the indiscernibility-type incompleteness of information in rough set analysis. In this paper we consider the question when a dependence space can be locally approximated by a approximation space. We introduce a concept of (weakly) local approximation spaces and establish several important relationships among equivalences, reducts, and sub-reducts with respect to (weakly) local approximation spaces. It is shown that a dependence space is a local approximation space if and only if it is locally reducible if and only if the closure lattice generated by the dependence space is an atomic lattice. This result also gives a partial solution to an open problem posed by M. Novotný.