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.     

Predicting the extension of equivalence classes from primary generalization gradients: the merger of equivalence classes and perceptual classes.

In Experiment 1, 6 college students were given generalization tests using 25 line lengths as samples with a long line, a short line, and a “neither” option as comparisons. The neither option was to be used if a sample did not go with the other comparisons. Then, four-member equivalence classes were formed. Class 1 included three nonsense words and the short line. Class 2 included three other nonsense words and the long line. After repeating the generalization test for line length, additional tests were conducted using members of the equivalence classes (i.e., nonsense words and lines) as comparisons and intermediate-length lines as samples. All Class 2 comparisons were selected in the presence of the test lines that also evoked the selection of the long line in the generalization test that had been given before equivalence class formation. Class 1 yielded complementary findings. Thus, the preclass primary generalization gradient predicted which test lines acted as members of each equivalence class. Regardless of using comparisons that were nonsense words or lines, the post-class-formation gradients overlapped, showing the substitutability of class members. Experiment 2 assessed the discriminability of the intermediate-length test lines from the Class 1 (shortest) and Class 2 (longest) lines. The test lines that functioned as members of an equivalence class were discriminable from the line that was a member of the same class by training. Thus, these test lines also acted as members of a dimensionally defined class of “long” or “short” lines. Extension of an equivalence class, then, involved its merger with a dimensionally defined class, which converted a close-ended class to an open-ended class. These data suggest a means of predicting class membership in naturally occurring categories.     

The structure of equivalence classes

THE STRUCTURE OF EQUIVALENCE CLASSES CAN BE COMPLETELY DESCRIBED BY FOUR PARAMETERS: class size, number of nodes, the distribution of "singles" among nodes, and directionality of training. Class size refers to the number of stimuli in a class. Nodes are stimuli linked by training to at least two other stimuli. Singles are stimuli linked by training to only one other stimulus. The distribution of singles refers to the number of singles linked by training to each node. Directionality of training refers to the use of stimuli as samples and as comparison stimuli in training. These four parameters define the different ways in which the stimuli in a class can be organized, and thus provide a basis for systematically characterizing the properties of stimuli in a given equivalence class. The four parameters can also be used to account for the development of individual differences that are commonly characterized in terms of "understanding" and connotative meaning.Methods are described for generating all possible combinations of parameter values, and a formula is introduced which specifies all of the parameter values for an equivalence class. Its utility for interrelating experimental procedures is demonstrated by analyzing a number of representative experiments that have addressed equivalence-class formation.