We are studying joint activity in which a remote robot finds an object by commnnicating with the user over a voice-only channel. We focus on how the robot disambiguates the reference of the uttered word or phrase to the target object. For example, by "cup", one may refer to a "teacup", a "coffee cup", or even a "glass" under some situations. This reference (hereafter, "object reference") is user-dependent. We confirm that a user model of object references is significant by conducting a survey of 12 subjects. In addition to ambiguity of object reference, actual systems should cope with two other sources of uncertainty in speech and image recognition. We present a Belief Network based probabilistic reasoning system to determine the object reference. The resulting system demonstrates that the number of interactions needed to find a common reference is reduced as the user model is refined.