Nodal Structure and the Partitioning of Equivalence Classes

Abstract

By definition, all of the stimuli in an equivalence class have to be functionally interchangeable with each other. The present experiment, however, demonstrated that this was not the case when using post-class-formation dual-option response transfer tests. With college students, two 4-node 6-member equivalence classes with nodal structures of A-->B-->C-->D-->E-->F were produced by training AB, BC, CD, DE, and EF. Then, unique responses were trained to the C and D stimuli in each class. The responses trained to C generalized to B and A, while the responses trained to D generalized to E and F. Thus, each 4-node 6-member equivalence class was bifurcated into two 3-member functional classes: A-->B-->C and D-->E-->F, with class membership precisely predicted by nodal structure. A final emergent relations test documented the intactness of the underlying 4-node 6-member equivalence classes. The coexistence of the interchangeability of stimuli in an equivalence class and the bifurcation of such a class in terms of nodal structure was explained in the following manner. The conditional discriminations that are used to establish a class also imposes a nodal structure on the stimuli in the class. Thus, the stimuli in the class acquire two sets of relational properties. If the format of a test trial allows only one response option per class, responding on those trials will be in accordance with class membership and will not express the effects of nodal distance. If the format of a test trial allows more than one response option per class, responding on those trials will be determined by the nodal structure of the class. Thus, the relational properties expressed by the stimuli in an equivalence class are determined by the discriminative function served by the format of a test trial.

An “Orwellian” Account of Stimulus Equivalence. Are Some Stimuli “More Equivalent” Than Others?

“…Transfer decreases with nodal distance and increases with delayed matching training. This differential transfer is compatible with the notion that equivalent stimuli may differ in their degree of relatedness, as claimed by Fields and colleagues (e.g., Belanich & Fields, 2003;Fields et al, 1995;Fields & Watanabe-Rose, 2008). Fields and colleagues argued that relatedness is a function of nodal distance.…”

“…Equality is an equivalence relation, and an equivalence relation could not admit degrees. However, Lanny Fields and colleagues have argued, without irony, that equivalence relations between stimuli may be established in different degrees or, in other words, members of a class of equivalent stimuli may have different degrees of relatedness between themselves (e.g., Belanich & Fields, 2003;Fields et al, 1993;Fields et al, 1995;Fields & Watanabe-Rose, 2008).…”

“…A more recent study addressing this question was conducted by Fields and Watanabe-Rose (2008). They established two six-member equivalence classes, training conditional discriminations AB, BC, CD, DE, and EF.…”

Assessment of the Relatedness of Equivalent Stimuli Through a Semantic Differential

“…Tests of emergent relations conducted with matching-to-sample procedures could not reveal such differences: Matching tests can reveal the presence of an emergent relation but not any possible difference in the degree of relatedness. Different degrees of relatedness can be revealed, however, by other measures, such as latency (Fields & Moss, 2008) or transfer of functions (Fields & Watanabe-Rose, 2008). The methodology described here seems to be very sensitive to revealing such effects.…”

Sorting: An Alternative Measure of Class Formation?

“…In contrast, the same test trials presented to other participants produced classindicative responding only after extended testing, thereby documenting the delayed emergence of the equivalence classes (e.g., Fields and Watanabe-Rose 2008;Holth and Arntzen 1998;Kennedy 1991).…”