Chapter 1, 'Compositionality, Flexibility, and Context Dependence', covers the essential second step in the NP--accounting for how the postulation of widespread context dependence is compatible with compositionality, the usual explanation for our ability to understand a potentially open-ended class
of novel utterances.
Students classified as dualists by Perry's scheme were better able to contribute to class discussions when guided by scenarios rather than completely open-ended class
discussions, because the scenarios provided more structure (Grossman, 1994).
An open-ended class consists of contiguous stimuli along some continuum, all of which occasion the same response that has been trained to one or a few of the stimuli in that range (Cook, Wright, & Krendrick, 1990; Fields & Reeve, 2001; Goldiamond, 1966; Hull, 1920; Keller & Schoenfeld, 1950; Lea, 1984; Reeve & Fields, 2001; Wasserman et al., 1988; Wright, Cook, Rivera, Sands, & Delius, 1988).
According to mutual selection, the variants that are members of an open-ended class would be those that occasion the selection of the base stimulus during the variant-to-base tests and are also selected in the presence of the same base stimulus during the base-to-variant tests.
An open-ended class is the broadest range of stimuli that occasion the same response.
In a generalized equivalence class, the perceptually disparate stimuli function as members of an equivalence class, and the physically similar stimuli function as members of an open-ended class. All of the stimuli in both of these classes become related to each other because one stimulus serves as a member of both the equivalence class and the open-ended class (Fields, Adams, Brown, & Verhave, 1993).
A generalized equivalence class can be established by the formation of an equivalence class among the physically disparate stimuli, the formation of an open-ended class among the stimuli that are dimensional variants of each other, and the inclusion of one stimulus as a member of both classes (Fields, Reeve, Adams, & Brown, & Verhave, 1997).
If all of the images in the basal equivalence class and the open-ended class occasion the mutual selection of all other members of both classes, collectively, they would constitute a generalized equivalence class.
Thus, a close-ended equivalence or functional class became an open-ended class
. Indeed, any close-ended category can be converted to an open-ended class
A disadvantage of having open-ended classes is that we cannot compute some types of averages and measures of dispersion such as the arithmetic mean, midrange and standard deviation, and range from the frequency distribution.
However, the mean is difficult, if not impossible, to calculate when the frequency distribution contains open-ended classes. These do not affect the other two averages.
It is quite useful, however, when we must compute an average for a frequency distribution with open-ended classes and we need a measure of dispersion to go with it.