The present research tested the hypothesis that on-line language processing is guided by gradient representations of linguistic common ground that reflect details of how common ground was established, including the discourse context and partner feedback. This hypothesis was contrasted with a simpler hypothesis that interpretation processes are only sensitive to simple binary representations of whether a potential discourse referent is or is not common ground. In order to evaluate these hypotheses, participants engaged in a task-based conversation with an experimenter in which some of the participant's game-pieces were hidden from the experimenter. On critical trials, the participant revealed the identity of the hidden game-pieces. Critical utterances contained referring expressions temporarily ambiguous between a visually shared game-piece, and a hidden game-piece. Analysis of participant eye movements during interpretation of these utterances revealed that participants were more likely to consider the hidden game-piece a potential referent if the experimenter had initially asked about its identity; whether the experimenter provided clear feedback that s/he understood its identity modulated this effect somewhat. These results provide key evidence for the richness of common ground representations, and are discussed in terms of the implications for models of the underlying representations of common ground.