A Methodological Integration of Generalized Equivalence Classes, Natural Categories, and Cross-Modal Perception

Emergent categorization in the recognition of black and white paintings through conditional discrimination

Background

The emergent categorization involving paintings by renowned painters and their corresponding names was demonstrated by previous studies. However, the results of these studies suggest that the colors of the pictures may have played a preponderant role, obscuring other aspects of the stimuli that could be more directly related to the style of each painter. To verify this possibility, the present study used the same methodology of Ferreira et al. to investigate the establishment of emergent conditional relations between categories composed of black and white paintings and the names of their authors.

Method

The procedure consisted of the training of relations between each of the ten paintings and an abstract picture, for each of the three painters Botticelli, Monet, and Picasso. Relations between each of the three abstract figures and the printed name of one of the painters were verified in sequence. Finally, tests of relations between five trained and five untrained paintings of each artist and the printed names were conducted.

Results

The participants’ performance suggests that the outcome was properly controlled by aspects pertinent to the paintings that belonged to each painter’s category.

Conclusions

The results reinforced the data obtained previously with colored pictures, suggesting that the process of emergent categorization involving artificial categories of paintings is robust. It also indicates possibilities for future investigations, for example, using stimuli of other artistic productions, such as sculpture and music.

Generalization of equivalence relations from photos to objects by preschool children

Generalized equivalence classes are stimulus classes that consist of equivalent stimuli and other physically similar class-member stimuli. The present study evaluated whether preschool children would form equivalence classes among photos of abstract objects (2D) and show equivalence generalization to the corresponding objects (3D), printed photos (2D stimuli), and to black-and-white drawn pictures (2D stimuli). Six typically developing children were taught arbitrary relations to establish three 3-member equivalence classes with 2D stimuli presented on a computer screen. AB-AC baseline relations (for half of the participants) and AB-BC relations (for the other half) were taught using a multiple-probe design to assess taught and tested relations. After class formation, three types of generalization probes were conducted: generalization to 3D stimuli, generalization between 2D (printed photos) and 3D stimuli, and generalization to drawn pictures (2D). All of the participants formed the equivalence classes. Two participants met the criterion for all three generalization probe types. Two participants presented mixed results across tests, and two participants did not exhibit equivalence generalization. The results demonstrated equivalence generalization from 2D to 3D stimuli in preschool children, although the variability across participants suggests that such generalization cannot be assumed a priori.

Meaningful Stimuli and the Enhancement of Equivalence Class Formation

Stimulus meaningfulness has been defined by its hedonic valence, denotative (definitional) and connotative (evaluative) properties, and its influence on forming categories called equivalence classes. Positive or negative hedonic value of a meaningful stimulus transfers to the other members of an equivalence class that contains such a stimulus, and also influences likelihood of class formation. The denotative and connotative properties of meaningful stimuli are instantiated by the responses they produced (simple discriminative functions) and by the selection of other related words (conditional discriminative functions). If a meaningless cue acquires one such stimulus control function, and is included in a set of otherwise meaningless stimuli, its inclusion enhances the formation of an equivalence class. These results suggest ways to enhance equivalence class formation in applied settings. When degree of enhancement matches that produced by the inclusion of a meaningful stimulus in a class, class enhancement can be accounted for by the stimulus control functions it serves, as well as its hedonic, denotative, and connotative properties. We also linked equivalence class formation and meaningfulness to semantic networks, relational frame theory, verbal behavior, and naming.

All stimuli are equal, but some are more equal than others: measuring relational preferences within an equivalence class

Two experiments used post-class formation within-class relational assessment test performances to evaluate whether participants demonstrated preference for certain members of an equivalence class based on the type of relation that existed between class members. In Experiment 1, two 5-node 7-member equivalence classes, consisting entirely of nonsense syllables, were established using the simultaneous protocol. Only 1 of the 6 participants in Experiment 1 formed classes. After class formation, the effects of the different relations between stimuli were evaluated using within-class relational assessment tests, and the 1 participant showed an absolute preference for transitive over equivalence relations, and for baseline over symmetrical relations. Experiment 2 was identical to Experiment 1, except that one of the nonsense syllable stimuli in each class was replaced by a pictorial stimulus. Under these conditions, classes were formed by 5 of 13 participants. During the relational assessment tests, the 5 participants who formed classes demonstrated almost exclusive preferences for transitive relations over equivalence relations and for trained baseline relations over symmetrical relations. Thus, this research demonstrates that the members of equivalence classes are differentially related to each other based on relational type.

Emergence of untaught mands or tacts of novel adjective-object pairs as a function of instructional history

We tested the effects of multiple exemplar instruction (MEI) on the emergence of untaught mands or tacts of adjective-object pairs in a multiple-probe design across four students with autism/developmental disabilities. None of the students emitted either mands or tacts for three sets of three adjective-object pairs (word sets counterbalanced across students and conditions) in pre-experimental probe trials. In the baseline phase, either mands or tacts were taught for the first adjective-object pairs to each student who then received probe trials for the untaught verbal operants. None of the students emitted the verbal operant that was not directly taught. In the MEI condition, a second set of adjective-object pairs was taught under alternating mand and tact conditions until both operants were mastered. Following mastery of the second set in the MEI condition, students were again probed for the untaught mands or tacts for the adjective-object pairs that were not in their repertoires when a single verbal operant was taught in baseline (the first set). All students emitted the untaught mands or tacts for the first set. Finally, a third set of adjective-object pairs was taught as tacts or mands and the untaught mands or tacts emerged. The data are discussed in terms of generative verbal behavior, abstraction of establishing operation control, and multiple exemplar instruction.

Effects of a meaningful, a discriminative, and a meaningless stimulus on equivalence class formation

Thirty college students attempted to form three 3-node 5-member equivalence classes under the simultaneous protocol. After concurrent training of AB, BC, CD, and DE relations, all probes used to assess the emergence of symmetrical, transitive, and equivalence relations were presented for two test blocks. When the A-E stimuli were all abstract shapes, none of 10 participants formed classes. When the A, B, D, and E stimuli were abstract shapes and the C stimuli were meaningful pictures, 8 of 10 participants formed classes. This high yield may reflect the expansion of existing classes that consist of the associates of the meaningful stimuli, rather than the formation of the ABCDE classes, per se. When the A-E stimuli were abstract shapes and the C stimuli became S(D)s prior to class formation, 5 out of 10 participants formed classes. Thus, the discriminative functions served by the meaningful stimuli can account for some of the enhancement of class formation produced by the inclusion of a meaningful stimulus as a class member. A sorting task, which provided a secondary measure of class formation, indicated the formation of all three classes when the emergent relations probes indicated the same outcome. In contrast, the sorting test indicated "partial" class formation when the emergent relations test indicated no class formation. Finally, the effects of nodal distance on the relatedness of stimuli in the equivalence classes were not influenced by the functions served by the C stimuli in the equivalence classes.

Evaluating merger and intersection of equivalence classes with one member in common

Sidman (1994) noted that the existence of a member that is common to more than one class may produce either class merger (union) or class intersection. A multiple-selection, matching-to-sample test was developed to examine the conditions under which these outcomes occur. Test trials each required three conditional discriminations involving selection or rejection of comparison stimuli under control of samples representing two categories. Test results obtained from an initial group of typical adults using familiar stimuli (DOG and BIRD, pictures of dogs and birds and relevant printed breed names (e.g., DALMATIAN, RETRIEVER) showed the conditional stimulus control best described as intersection. For example, the word DALMATIAN provided the context for selecting the dalmatian but not the retriever picture. However, these results may have depended on the participants' verbal history as English speakers. Would conditional-discrimination training with overlapping sets of laboratory-generated stimuli also result in intersection? Naïve typical adults were assigned to one of three different training conditions. Like the participants tested with familiar stimuli, these participants demonstrated highly reliable test outcomes best described as showing class intersection, regardless of training condition. These findings begin to elucidate the necessary and sufficient conditions for establishing complex category-like classes of stimuli.

Equivalence class formation: a method for teaching statistical interactions

Many students struggle with statistical concepts such as interaction. In an experimental group, participants took a paper-and-pencil test and then were given training to establish equivalent classes containing four different statistical interactions. All participants formed the equivalence classes and showed maintenance when probes contained novel negative exemplars. Thereafter, participants took a second paper-and-pencil test. Participants in the control group received two versions of the paper-and-pencil test without equivalence-based instruction. All participants in the experimental group showed increased paper-and-pencil test scores after forming the interaction-indicative equivalence classes. Class-indicative responding also generalized to novel exemplars and the novel question format used in the paper-and-pencil test. Test scores did not change with repetition for control group participants. Implications for behavioral diagnostics and teaching technology are discussed.

Equivalence class formation in a trace stimulus pairing two-response format: effects of response labels and prior programmed transitivity induction

Three experiments identified factors that did and did not enhance the formation of two-node four-member equivalence classes when training and testing were conducted with trials presented in a trace stimulus pairing two-response (SP2R) format. All trials contained two separately presented stimuli. Half of the trials, called within-class trials, contained stimuli from the same class while the other half, called cross class trials, contained stimuli from different classes. On within class trials, making a YES response was correct and making a NO response was wrong. On cross class trials, making a NO response was correct and making a YES response was wrong. In Experiment 1, similar intermediate percentages of participants (about 50%) formed classes, regardless of whether the responses were labeled YES and NO or SAME and DIFF. Response labeling thus did not influence class formation. Regardless of response labels, failures of class formation were primarily due to failure of class-indicative responding produced by within-class transitivity probes. In Experiment 2, only 50% of participants formed classes without prior training, as in Experiment 1, but 100% of participants formed equivalence classes after the establishment of a generalized transitivity repertoire by use of a programmed transitivity induction protocol. Experiment 3 examined two components of the programmed transitivity induction protocol and found that the exclusion of AC trials had no effect on the percentage of participants who formed equivalence classes, while presenting the stimulus sets in randomized order interfered with equivalence class formation. A further analysis found that a number of stimulus control topographies differentiated between individuals who did and did not form equivalence classes. In general, then, these experiments demonstrate that equivalence classes can be formed reliably when training and testing are conducted in an SP2R format, supporting the view that equivalence class formation can account for the development of conceptual categories in natural settings.

Optimizing linked perceptual class formation and transfer of function

A linked perceptual class consists of two distinct perceptual classes, A' and B', the members of which have become related to each other. For example, a linked perceptual class might be composed of many pictures of a woman (one perceptual class) and the sounds of that woman's voice (the other perceptual class). In this case, any sound of the woman's voice would occasion the selection of any picture of the woman and vice versa. In addition, after learning to name the woman in the presence of one picture, that name would be uttered when presented with all of the images of the woman's face and all of the sounds of her voice. This study involved 15 participants and sought to (a) maximize the percentage of participants who formed linked perceptual classes, and (b) determine whether those classes acted as transfer networks, that is, whether the discriminative function of one class member would generalize to other members of the class and not to members of a different class. The rate of emergence of each linked perceptual class was maximized by establishing a single class-linking conditional relation between the clearest member of one class used as a sample stimulus and the most ambiguous member of the other class used as a comparison stimulus. Class formation was demonstrated using the serial and programmed presentation of A'-B' probes that consisted of untrained pairs of stimuli drawn from the A' and B' classes. Most participants showed immediate emergence of the two linked perceptual classes. The remaining participants showed delayed emergence following a second exposure to each originally error-producing probes. Once the linked perceptual classes had emerged, a differential response to a specific member of one perceptual class generalized mostly or completely to the other members of that linked class and rarely, if ever, to members of the other linked class. Thus, generalization did not depend on the specific class members that had been used for discrimination training.

Formation of partially and fully elaborated generalized equivalence classes

Most complex categories observed in real-world settings consist of perceptually disparate stimuli, such as a picture of a person's face, the person's name as written, and the same name as heard, as well as dimensional variants of some or all of these stimuli. The stimuli function as members of a single partially or fully elaborated generalized equivalence class when they occasion the mutual selection of each other after the establishment of some subset of relations among the stimuli. Indeed, it is these generalized relations among stimuli that enable an individual to respond appropriately to the inevitable flux of natural environments. The present experiments involved procedures for producing both types of generalized equivalence class and for evaluating their retention. Granting the formal and functional similarities that exist between generalized equivalence classes and natural categories, natural kinds, and fuzzy superordinate classes, the variables responsible for the emergence of the former might also account for the emergence of the latter three phenomena. In Experiment 1, After forming an A'-B' class, a B'-C relation was trained and generalization tests were conducted with B'-C, C-B', A'-C, and C'-A. Two of 5 participants passed the tests documenting the formation of A'-B'-C classes. Failures occurred in the A'-C and C-A' tests but not the B'-C and C-B' tests. Failures were also correlated with time between A'-B' class formation and C-based testing and with the absence of baseline confirmation when training and testing were separated by about one week. Experiment 2 replicated Experiment 1 but presented baseline confirmation probes immediatley prior to testing when training and testing were separated by one week; all participants then formed partially elaborated generalized equivalence classes. In Experiment 3, 5 of 6 participants formed fully elaborated generalized equivalence classes, represented as A' = B' = C'.

Concept formation based on value relations evaluated with a matching-to-sample procedure

To study concept formation based on relations, adults were taught and tested on complex discriminations involving figures that varied in colors, forms, and orientations. In Experiment 1, participants learned to select figures with values A1 and B1 or values B1 and C1; thereafter, they consistently selected figures with values A1 and C1. Selections were based on the relations among the values, rather than on perceptual properties. Experiments 2 and 3 studied generalization with a matching-to-sample procedure: participants learned to select "yes" in the presence of the positive figures, such as A1B1, and "no" in the presence of the negative figures. Thereafter, all figures that resulted from combining three values of the three relevant dimensions were probed. Participants typically selected "yes" in the presence of the novel figures that had two or three values related to one another and selected "no" in the presence of the other figures. Finally, two participants learned a simple discrimination. They did not generalize responding to other figures with the same values; instead, their performance in the generalization test remained almost unaltered. Thus, the concept based on relations was not affected by the simple discrimination. These results showed some unique properties of the concept based on relations and challenge previous theories on concept formation.

Equivalence relations, contextual control, and naming

This paper reports two experiments that investigated the role of verbal behavior in the emergence and generalization of contextually controlled equivalence classes. During both experiments, participants were trained with two different combinations of the same easily nameable, yet formally unrelated, pictorial stimuli. Match-to-sample baselines for eight four-member classes were established under the contextual control of two colors. In the presence of one color, conditional relations were established between stimuli whose normative names rhymed. In the presence of the other color, conditional relations were established between stimuli whose normative names did not rhyme. Although, during Experiment 1, all participants demonstrated equivalence classes involving rhyming stimuli, none demonstrated the formation of nonrhyme equivalence classes. To investigate this finding, Experiment 2 evaluated whether participants would demonstrate both rhyme and nonrhyme equivalence classes given more extensive exposure to the experimental contingencies. All participants demonstrated contextually controlled rhyme and nonrhyme equivalence classes, although rhyme classes were demonstrated with greater facility than nonrhyme classes. Results indicate that visual stimuli are named, that verbal bases for stimulus classification can affect the emergence of contextually controlled equivalence classes, and that untrained contextually controlled conditional discriminations involving novel stimuli can emerge on the basis of participants' verbal behavior.

The effects of differential training procedures on linked perceptual class formation

When the stimuli in one perceptual class (A') become related to the stimuli in another perceptual class (B'), the two are functioning as a single linked perceptual class. A common linked perceptual class would be the sounds of a person's voice (class A') and the pictures of that person (class B'). Such classes are ubiquitous in real world settings. We describe the effects of a variety of training procedures on the formation of these classes. The results could account for the development of naturally occurring linked perceptual classes. Two perceptual classes (A' and B') were formed in Experiment 1. The endpoints of the A' class were called anchor (Aa) and boundary (Ab) stimuli. Likewise, the anchor and boundary stimuli in the B' class were represented as Ba and Bb. In Experiment 2, the A' and B' classes were linked by the establishment of one of four cross-class conditional discriminations: Aa-->Ba, Aa-->Bb, Ab-->Ba, or Ab-->Bb. Results were greatest after Aa-->Bb training, intermediate after Aa-->Ba and Ab-->Ba training, and lowest after Ab-->Bb training. Class formation was influenced by the interaction of the anchor/boundary values and the sample/comparison functions of the stimuli used in training. Experiment 3 determined whether class formation was influenced by different sets of two cross-class conditional discriminations: Aa-->Ba and Ab-->Bb, or Aa-->Bb and Ab-->Ba. Both conditions produced equivalent results. Similarities were attributable to the use of anchor stimuli as samples and boundary stimuli as comparisons in each training condition. Finally, the results afterjoint Aa-->Ba and Ab-->Bb training were much greater than those produced by summing the results of Aa-->Ba training alone and Ab-->Bb training alone. This same synergy was not observed after joint Aa-->Bb and Ab-->Ba training or either alone.

The effect of test schedules on the formation of linked perceptual classes

After training conditional discriminations among selected stimuli from two perceptual classes, the emergence of novel relations involving other members of both classes was assessed using cross-class probes. The cross-class probes were presented using one of four different testing schedules. In the 2/9 test, nine different probes were presented in each of two test blocks. In the 6/3 test, three different probes were presented in each of six test blocks. In the 18/1-RND test, each of the 18 cross-class probes was presented in separate test blocks. In the 2/9 and 6/3 tests, the cross-class probes were presented in a randomized order within test block. In the 18/1-RND test, the cross-class probes were presented in a randomized sequence. In the 18/1-PRGM test, however, the cross-class probes were presented in a programmed order (i.e., the values of the stimuli in each cross-class probe were changed systematically in the succession of probe presentations). About 55% of the linked perceptual classes emerged during the 2/9, 6/3, and 18/1-RND tests. Thus the number of different probes in a test block did not influence the emergence of classes as long as the probes were presented in a random order. Virtually all classes emerged during the 18/1-PRGM test. Thus at least one ordered introduction of different cross probes resulted in the reliable emergence of linked perceptual classes. Mechanisms responsible for linked perceptual class formation are discussed along with the relation of these classes to other complex categories.

The formation of linked perceptual classes

Multiple-exemplar training with stimuli in four domains induced two new fill-based (A1' and A2') and satellite-image-based (B1' and B2') perceptual classes. Conditional discriminations were established between the endpoints of the A1' and B1' classes as well as the A2' and B2' classes. The emergence of linked perceptual classes was evaluated by the performances occasioned by nine cross-class probes that contained fill variants as samples and satellite variants as comparisons, along with nine other cross-class probes that consisted of satellite variants as samples and fill variants as comparisons. The 18 probes were first presented serially and then concurrently. Class-consistent responding indicated the emergence of linked perceptual classes. Of the linked perceptual classes, 70% emerged during the initial serial test. An additional 20% of the linked perceptual classes emerged during the subsequently presented concurrent test block. Thus, linked perceptual classes emerged on an immediate or delayed basis. Linked perceptual classes, then, share structural and fuctional similarities with equivalence classes, generalized equivalence classes, cross-modal classes, and complex maturally occurring categories, and may clarify processes such as intersensory perception.

The formation of a generalized categorization repertoire: effect of training with multiple domains, samples, and comparisons

The present experiment explored the effects of three variables on the spontaneous categorization of stimuli in perceptually distinct and novel domains. Each of six stimulus domains was created by morphing two images that were the domain endpoints. The endpoints of the domains were male and female faces, two abstract drawings, a car and a truck, two banded-elevation satellite land images, a tree and a cat, and two false-color satellite images. The stimulus variants at each end of a domain defined two potential perceptual classes. Training was conducted in a matching-to-sample format and used stimuli from one or two domains, one or three variants per class as samples, and one or three variants per class as comparisons. The spontaneous categorization of stimuli in the untrained stimulus domains showed the emergence of a generalized categorization repertoire. The proportion of spontaneously categorized stimuli in the new domains was positively related to the number of domains and samples used in training, and was inversely related to the number of comparisons used in training. Differential reaction times demonstrated the discriminability of the stimuli in the emergent classes. This study is among the first to provide an empirical basis for a behavior-analytic model of the development of generalized categorization repertoires in natural settings.