In this paper I discuss the notion of accessibility in dynamic semantics an
d develop a refinement of the accessibility relation, which pays special at
tention to the description expressed in the anaphoric expression and the pr
ogression in a discourse. Anaphoric expressions are interpreted as referrin
g to the most accessible item of their kind. I employ choice functions as t
he formal means to represent this accessibility relation. This element repr
esents the most-accessible of its kind in a particular discourse. Linguisti
c expressions do not only depend in their interpretation on the accessibili
ty structure of a discourse, they also change this structure. The referent
of an indefinite NP becomes the most accessible item of its kind. This chan
ge of the accessibility is modelled by updates of choice functions as an ad
ditional level of meaning. It will be shown that this extended formalism yi
elds not only a more adequate representation of discourses, but also solves
the problem of how to establish anaphoric links and supplies a uniform rep
resentation of definite and indefinite expressions with respect to their po
tential to change the accessibility structure of the discourse.