Lanny Fields

Enhancing Equivalence Class Formation by Pretraining of Other Equivalence Classes

This study investigated how the learning of one set of equivalence classes enhances the learning of new equivalence classes. Fifty-two undergraduate students were divided into four groups. Subjects in Group 1 received no pretraining. Using the simple-to-complex procedure followed by incremental expansion of class size, subjects in Groups 2, 3, and 4 learned 3-, 4-, and 5-member equivalence classes, respectively. After pretraining, two new 3-member equivalence classes were established by the concurrent training of all baseline relations and the concurrent presentation of all emergent relations probes to assess class formation (the simultaneous protocol). With no pretraining, 58% of subjects formed the new classes under the simultaneous protocol. After pretraining of the 3-, 4-, and 5-member classes, the new classes were formed by 62, 85, and 100% of the subjects, respectively. Pretraining of 4- and 5-member classes produced a small increment in the percentage of subjects who showed the immediate emergence of the new classes. Pretraining of the 5-member classes produced a large increment in percentage of subjects who formed classes with repeated testing. Thus, pretraining influenced immediate and delayed emergence of equivalence classes.With no pretraining, during the tests used to assess the formation of the new classes, 12% of subjects showed disruption of baseline performances, relational responding produced by symmetry probes was lower than that produced by baseline relations, and very low levels of relational responding were evoked by 1-node probes. These data demonstrated the effects of nodal distance. Pretraining did not ameliorate the disruption of baseline performances. Pretraining of 4- and 5-member classes produced moderate increments in the relational responding evoked by symmetry probes. Pretraining of 5-member classes produced large increments in the relational responding evoked by 1 -node probes.

Contextual Control of New Equivalence Classes

This study describes a method which allows for the unambiguous measurement of contextual control of equivalence class membership. Two equivalence classes, Ai-Bi-Ci and Aj-Bj-Cj, were formed by training Ai-Bi, Bi-Ci, Aj-Bj, and Bj-Cj in the presence of a short line denoted by X. In a subsequent test, all relations were displayed in the presence of a long line denoted by Y, to see if performances would indicate the emergence of the alternative classes Ai-Bj-Cj and Aj-Bi-Ci. If they did not emerge, Ai-Bj, Bj-Cj, Aj-Bi, and Bi-Ci were trained in the presence of Y, and the emergent relations test performances indicated the development of the alternative classes. This three-stage cycle was repeated with new sets of stimuli until the alternative classes emerged during the initial tests conducted in the presence of Y for two consecutive sets of new stimuli. This occurred after training with 4, 6, and 12 new classes for three of the five subjects. These outcomes could not be accounted for in terms of compound or multielement stimulus control because the contextual stimuli influenced membership in new equivalence classes. These results, then, provided an unequivocal demonstration of contextual control over the membership of stimuli in new equivalence classes. Finally, performances occasioned by primary generalization tests showed that contextual control extended to many lines that were similar in length to those used as the X and Y stimuli. These contingency-based performances have the formal appearance of rule-governed behavior.

Response Transfer between Stimuli in Generalized Equivalence Classes: A Model for the Establishment of Natural Kind and Fuzzy Superordinate Categories

Two equivalence classes were formed by college students through training of Ab, Bc, and Cd relations. The A, B, and C stimuli in both classes were nonsense words. The D stimulus in Class 1 was a short line; the D stimulus in Class 2 was a long line. Post-class-formation generalization tests of emergent relations were conducted to determine which intermediate length lines (variants of the D stimuli) also acted as class members. Those variants and the A, B, C, and D stimuli formed a generalized equivalence class. After different responses were trained to the A1 and A2 stimuli, the response trained to the A1 stimulus transferred to the other Class-1 stimuli and the response trained to the A2 stimulus transferred to the other Class-2 stimuli. Responding also transferred to the variants that acted as members of each generalized equivalence class, indicating that the stimuli in each generalized equivalence class also acted as members of a corresponding functional class. For the line variants that were members of a generalized equivalence class, response transfer from the A stimuli was very highly predicted from the generalization gradients of the emergent relations. The processes that account for the formation of a generalized equivalence class and the transfer of responding between members of such a class will be used to account for the development of natural kind and superordinate fuzzy categories.

Interactions among emergent relations during equivalence class formation

The interactions among symmetry, transitivity, and equivalence tests during the formation of 3-member equivalence classes were studied with 14 college students. After training AB and BC, a test with BA, CB, AC, and CA was conducted concurrently. Failure led to serial testing with probes for CA equivalence, BA symmetry, CA equivalence, CB symmetry, CA equivalence, AC transitivity, and CA equivalence. For five subjects, equivalence tests were passed immediately once BA and CB symmetry as well as AC transitivity had been induced. Thus, symmetry and transitivity were precursors for successful performance on equivalence tests. The conjoint function of symmetry and transitivity was assessed with the equivalence probes. As the equivalence probes were passed immediately, the presence of symmetry alone and transitivity alone were sufficient for their conjoint function without additional intervention. For different subjects, transitivity alone and symmetry were induced either directly with BA, CB, or AC probes or indirectly with equivalence probes. Equivalence probes can also induce various combinations of symmetry and transitivity. Thus, different subjects formed classes in various patterns at different rates.

The Expansion of Equivalence Classes Through Simple Discrimination Training and Fading

AB, BC, CD, and DE were established by conditional discrimination training. Symmetry, transitivity, and equivalence tests were then passed demonstrating the formation of 5-member equivalence classes. These tests were passed even though they were conducted in the absence of baseline relations. A new stimulus (F) was then linked to a class member (A) by stimulus fading conducted in the context of simple discrimination training. Thereafter, subjects passed FB, FC, FD, FE, BF, CF, DF, and EF tests, demonstrating that F functioned as a new member of the A-E class. The expansion of equivalence classes can also be accomplished by the use of simple discrimination training combined with stimulus fading, in addition to the typical use of conditional discrimination training. Equivalence classes, then, can be defined independently of conditional discrimination procedures.

Enhanced learning of new discriminations after stimulus fading

Humans learned to name three sets of braille patterns presented visually. After learning a practice set by traditional discrimination training, half the subjects learned a new set by fading, and the remaining subjects learned them by traditional discrimination training. Finally, all subjects learned a third set of new patterns by traditional discrimination training. Subjects who learned the second set by fading learned the third set faster than did subjects who learned the second set by traditional means. This effect was explained in terms of the differential strengthening of observing behavior by fading and by traditional discrimination training.