Agent state

The system performs a cycle of deciding and executing a strategy for a turn for a given mental state, and then updating that state using belief revision, and updating the dialogue history. On the user's turn, the cycle consists only of invoking the belief revision module and updating the dialogue history. The mental state consists of:

• Desires The desires of the agent are represented by intention rules, which give a probability distribution over parent intentions for a given plan. These can be used to describe intentions that are not explained within the plan that the agent is generating, but which are the starting point for a plan. For example, a travel agent may find that most passengers have a fixed intention to have a window seat in an aeroplane, and so do not seek to explain or change that intention within the dialogue. However, when the agent's plan is being recognised, this intention is added as a parent to the plan structure.

  While the intention rules describe a distribution over starting intentions, a utility function gives a value to each plan. It should be used to evaluate the different outcomes at the leaves of the game tree, producing a number, which is then used to compare different alternatives in the game tree. In section 2.13 it was stated that in planned dialogue, a compositional evaluation function is required that can be used on every element of the plan search space. Here, the two most important evaluation measures are taken, task completion and execution time, although others such as speech recognition error and response time are also compositional and can be used in the same way. Since evaluation is compositional, a recursive search of the plan structure is required that adds up all of the utility contributions of the acts in the plan. For task completion, the presence of the goal node in the complete plan is an indication of success, for which a positive utility is gained. Therefore the designer specifies a reward and goal node for the system. Each dialogue act is assumed to have some constant cost in terms of execution time. Therefore, the designer needs to specify this number for each of the terminals that appear in its plan rules. The system should search the plan structure automatically, using those given numbers. Finally, a weighted sum should be used, as in the PARADISE framework, to obtain an overall utility for the dialogue.

• Nested belief model The nested belief model is a numbered list of belief sets, where level 1 represents the acting agent's own beliefs. Level 2 represents its beliefs about the other agent, level 3 its beliefs about the other agent's beliefs about the acting agent, and so on. Only a finite number of levels is required, and this number equals the number of turns required in the dialogue. The utility functions of the agents ought to be nested as well, but for simplicity, they are assumed mutual, and therefore are outside the nested model.

• Belief set Each belief set is a set of propositions, paired with probability values. The probability value represents the estimate of the probability that the agent at that level holds that proposition. For example, a belief $p(prop,0.5)$ at level 3 represents the speaker's estimate of the hearer's estimate of the probability that the speaker holds the belief $prop$. Level 1 is distinguished from all others in that it represents the agent's own beliefs, which are not estimates. They therefore have probabilities of 0 or 1 only. The use of a probabilistic model of belief, rather than a logical one, follows from Harsanyi's model of the Bayesian game (see section 2.10), which allows for probability distributions over an agent's beliefs. By using a probabilistic model, the agent's estimated belief can be used. Typically, this estimated belief is informed by the evidence of previous dialogue, from which the frequency with which the belief occurred determines the probability value.

• Propositions Each proposition is of a particular type. There are domain propositions which represent the state of the environment. These propositions are just atomic propositions of predicate logic. There are plan rule propositions which represent the agent's capabilities - the plan rules that the agent believes are applicable, their preconditions and their effects. There are plan recognition rules which represent the probability that the agent intends a parent act given that a child act has occurred.