In this demonstration, a sequence of dialogues is processed by the system and the sequence of resulting belief states is recorded. Although acquisition happens at all levels of the belief state, beliefs remain mutual, so just the system's belief about whether the user intends a window seat, and the system's belief about whether the user believes the system has a window seat are recorded. The system starts in a state of [bel(have-seat),intend(window-seat)] = [0.5, 0.9], with the consequence that offering is dominant. The system's base belief was that it has a window seat. Contrary to the system's belief model, the stereotypical user does not want a window seat, and so as each user drawn from the stereotype refuses the offered seat, the belief state eventually crosses the decision surface, as the intention drops from precondition inference and the system begins to decline the initiative. Notice that the have-seat belief increases even though the user declines the initiative, since it is a precondition to offering. Once the system stops offering, the user continues to decline the initiative, and the system responds employing the dry-land algorithm to revise downwards both the user's intention to have a window seat and the user's belief that one is available.
Table 4.2:
Belief model states for a sequence of dialogues
