1 A Behavioral Model for Linguistic Uncertainty

Information is commonly transmitted through statements in natural language. The statement ‘Mary is young’, for instance, provides partial information about Mary’s age. If initially we know nothing about Mary’s age and we subsequently hear that she is young, our knowledge about her age has increased, although we remain uncertain about her exact age. In this paper we are concerned with the information conveyed by statements in natural language, which we call linguistic information. Linguistic information often involves vague predicates such as ‘young’. We will restrict our discussion to simple affirmative statements of the type ‘subject is predicate’ or ‘subject satisfies property’. The linguistic information ‘Mary is young’ produces some uncertainty about Mary’s age; it seems likely that Mary is younger than 30 years, but we cannot be certain about that. We will call this type of uncertainty linguistic uncertainty. In general, linguistic uncertainty is the uncertainty about a precisely defined quantity that is produced by linguistic information. The problem considered in this paper is how best to model linguistic uncertainty. In this problem, our uncertainty is due to a lack of knowledge, and not to some physical randomness or indeterminacy. Our model for linguistic uncertainty will therefore be epistemic rather than physical (see [42] for a discussion of this distinction). Why is this important? For one thing, linguistic uncertainty is very common and it is natural from a scientific or a philosophical point of view to attempt to model it. Another reason is more practical. Human actions are very often based on linguistic information. In order to design systems that emulate, “mechanize” or improve what humans do, it is therefore useful to be able to model this kind of information. For