Roles and values
An important aspect of Mental Spaces Theory is its treatment of NPs with definite interpretation, an issue that also relates to potential ambiguity. As we have seen, NPs of this kind include common nouns co-occurring with the definite article (the President) or proper nouns (James Bond). Mental Spaces Theory claims that NPs with definite interpretation do not have rigid reference, which means that they may or may not refer to a unique referent. This is illustrated by the following examples from Fauconnier (1994: 39):

The sentences in (8) are ambiguous. Example (8a) could mean that every seven years the person who is president changes in some way, for instance goes bald, becomes insane, grows a moustache and so on. Alternatively, (8a) could mean that every seven years the person who serves as president changes. Similarly, (8b) could mean that every time we see your car, some aspect of the car has changed; it might have had a respray, acquired some new hubcaps and so on. Alternatively, this sentence could mean that you have a new car every time we see you.
Ambiguities like these illustrate that NPs with definite interpretation can either have what Fauconnier calls a role reading or a value reading. For example, the role reading of the President relates to the position of president, regardless of who fills it (our second interpretation of (8a)). The value reading relates to the individual who fills the role (our first interpretation of (8a)). Roles and values both introduce elements into mental spaces, but each gives rise to different mapping possibilities. This is illustrated by example (9):

In the base, the elements Tony Blair, Prime Minister and Margaret Thatcher are all present. These are default elements established by the discourse or by encyclopaedic knowledge. This is indicated by the fact that they have definite reference, which shows that they are not set up as new elements but are preexisting. In this base, Tony Blair is a value element linked to the role element Prime Minister. In other words, there is a role-value relationship holding between the two elements, which are co-referential. This relationship could be established on the basis of background knowledge, but in (9) it is explicitly signalled by the first sentence. This relationship is captured in Figure 11.9 by the dotted arrows between the value element Tony Blair and the role element the Prime Minister. The second sentence sets up a new space, because it contains the space builder Margaret Thatcher thinks. . . . In Margaret Thatcher’s BELIEF space, she (which is linked to Margaret Thatcher by an identity connector) corresponds to the value element linked to the role element the Prime Minister, while Tony Blair corresponds to the value element linked to the role element the Leader of the Opposition. Figure 11.9 illustrates the interpretation of roles and values in example (9).
