1. Introduction to Vague Quantifiers

Talking about numbers of objects in a visual scene often involves the use of descriptions of quantity which are vague. Furthermore, quantifiers, whether they be of number (e.g., many), amount (e.g., much), or time/frequency (e.g., often) pervade natural language, and therefore constitute an essential part of the lexicon for the child to acquire, and consequently for integration into NL systems. An understanding of quantifiers is often largely couched in terms of the notion that quantifiers refer to points on a scale. In its most extreme form, the temptation is to treat quantifiers in terms of a quantifier-to-number mapping (e.g., Bass, Cascio & O’Connor, 1984; Reyna, 1981). In computational terms, a scene can be parsed for the number of entities present, and the mapping between the number and the quantifier associated with the appropriate point on the scale can be easily achieved. However, there is compelling evidence that the comprehension and production of quantifiers is affected by a range of variables which go beyond the number of objects present, including the relative size of the objects involved in the scene (e.g., Hormann, 1983, Newstead & Coventry, 2000), the expected frequency of those objects based on prior experience (e.g., Moxey & Sanford, 1993), the functionality present in the scene (Newstead & Coventry, 2000), and the need to control the pattern of inference of those involved in the communication (e.g., Moxey, Sanford & Dawydiak, 2001). To give an example of one of these context effects (expected frequency in this case), a few people outside a cinema is associated with more people than a few people outside a fire station (Moxey & Sanford, 1993).

The main aims of the grant were to develop a connectionist model of vague quantifier comprehension (extending the model for spatial language already developed on GR/N38145/01) which deals with both scalar and contextual components and maps onto real psycholinguistic data, and to establish empirically the relative extent to which these multiple constraints influence the comprehension of a range of quantifiers. The programme of work in practice remained faithful to these aims. However, during the literature review phase in the early months of the project it became clear that there is a lack of explanation in the literature for why context effects exist, and we were able to extend the theoretical coverage of the work in the grant by exploring the possibility that the origins of context effects may reside in visual processing of images. It has been assumed in the quantifier literature that the actual number of objects in a scene being described is the number used to map onto comprehension of vague quantifiers. Yet there is much evidence that, under time pressure conditions, people do not give very accurate judgments about the number of objects there are in a scene. When the number of objects in a visual scene rises beyond the “subitizing” range (i.e., >9 objects), we are much less accurate in our judgments of how many objects there are in a visual scene. In this grant we were able to show that the lack of success of scalar approaches to quantifiers, and the corresponding abandonment of this approach, has been a result of a conflation of number with the actual number of objects present. In the grant we were able to demonstrate that the “psychological” numbers returned from visual attentional constraints under time pressure allow number to predict the appropriateness of natural language quantifiers much more successfully. Specifically, across a range of experiments we uncovered a number of new context effects for vague quantifiers and showed that the same effects also occur for number judgments under time pressure. These experimental data permitted the design of a new connectionist model for the processing of visual scenes of groups of objects and the production of “psychological” quantifications and the selection of vague linguistic quantifiers. Furthermore, we were able to use the model to establish the extent to which language and number judgements bootstrap each other during learning.