Using a probabilistic belief model

In section 2.3, a logical model of belief was described, where an agent will regard any given proposition as either "believed", "disbelieved", or "possible". Using such a model agent A might come to believe that B believes P, should B inform A of P. For many dialogues such a model is adequate, and indeed most of the work seen in dialogue planning and user modelling described in chapter 2 rests upon a logical model of belief. However, more generally, it is better to know whether a belief is probable rather than merely possible. For example, if an agent were to plan a questioning dialogue, it might risk failure of the plan if the probability of the other agent not knowing the answer were small, but at some point the risk would be become large enough that the cost of trying the plan exceeds its expected reward. On the other hand, the logical model of belief cannot help to make such a judgement. A second advantage of a probabilistic model is that it can be used to estimate the beliefs of a population of users as a stereotype model. For example, if three of five users knew the answer to the question in the past, a reasonable estimate of the current user's knowledge is that he will give the answer in three of five outcomes. Similarly, if just one user sometimes holds a belief and sometimes does not, a probabilistic model is useful to form an expectation of that one user. The system can then make decisions based on the expected beliefs of the user.

A supposition is made now that the use of a probabilistic belief model offers significant gains in the efficiency of the dialogue, when expected utility is the objective. For this reason, a probabilistic model will be developed, and to verify this supposition, demonstration problems in the following chapters will be used to measure the efficiency of the dialogues obtained by a probabilistic planner.