Expansion of Sidman's theory: The inclusion of prompt stimuli in equivalence classes

Stimulus equivalence is defined as the ability to relate stimuli in novel ways after training in which not all of the stimuli had been directly linked to one another. Sidman (2000) suggested all elements of conditional discrimination training contingencies that result in equivalence potentially become class members. Research has demonstrated the inclusion of samples, comparisons, responses, and reinforcers in equivalence classes. Given the evidence that all elements of a conditional discrimination become part of the class, the purpose of this study was to determine if class-specific prompts would also enter into their relevant equivalence classes. Experiment 1 investigated the inclusion of prompts in an equivalence class using abstract stimuli with neurotypical students enrolled in higher education courses. Experiment 2 systematically replicated Experiment 1 using meaningful stimuli and individuals diagnosed with autism spectrum disorder. The results of both experiments demonstrated that class-specific prompts became part of equivalence classes with the other positive elements of the contingency. The results are discussed in terms of class expansion and the potential impact on equivalence-based instruction.     

Typicality effects in contingency-shaped generalized equivalence classes

Two experiments were conducted using match-to-sample methodologies in an effort to model lexical classes, which include both arbitrary and perceptual relations between class members. Training in both experiments used a one-to-many mapping procedure with nonsense syllables as samples and eight sets of abstract stimuli as comparisons. These abstract stimuli differed along a number of dimensions, four of which were critical to the experimenter-defined class membership. Stimuli in some comparison sets included only one of the class-defining features, but stimuli in other sets included two, three, or all four of the critical features. After mastery of the baseline training, three types of probe tests were conducted: symmetry, transitivity/equivalence, and novel probe tests in which the training nonsense syllables served as samples, and comparisons were novel abstract stimuli that included one or more of the class-defining features. Symmetry and transitivity/equivalence probe tests showed that the stimuli used in training became members of equivalence classes. The novel stimuli also became class members on the basis of inclusion of any of the critical features. Thus these probe tests revealed the formation of open-ended generalized equivalence classes. In addition, typicality effects were observed such that comparison sets with more critical features were learned with fewer errors, responded to more rapidly, and judged to be better exemplars of the class. Contingency-shaped stimulus classes established through a match-to-sample procedure thus show several important behavioral similarities to natural lexical categories.     

On the Logic of Classes as Many

The notion of a "class as many" was central to Bertrand Russell's early form of logicism in his 1903 Principles of Mathematics. There is no empty class in this sense, and the singleton of an urelement (or atom in our reconstruction) is identical with that urelement. Also, classes with more than one member are merely pluralities — or what are sometimes called "plural objects" — and cannot as such be themselves members of classes. Russell did not formally develop this notion of a class but used it only informally. In what follows, we give a formal, logical reconstruction of the logic of classes as many as pluralities (or plural objects) within a fragment of the framework of conceptual realism. We also take groups to be classes as many with two or more members and show how groups provide a semantics for plural quantifier phrases.     

Conceptualizing Media Stimuli in Experimental Research: Psychological Versus Attribute‐Based Definitions

This paper argues for a clearer conceptualization of media stimuli in experimental research and identifies 3 issues impeding our understanding of message processing: (a) assumptions bolstered by manipulation checks about homogeneity of response to media stimuli, (b) conflation of 2 different classes of variables—media attributes and psychological states, and (c) discrepancies between the conceptual model and operational‐level hypotheses used to test research questions. To provide a more comprehensive framework for investigating media effects in experimental research, we argue for a clearer conceptual separation between message attributes and user perceptions and apply a mediation model of information processing to overcome the limitations of conventional approaches. Subjected to 2 empirical tests involving the assessment of Web‐based media, the model finds an increase in explained variance in each instance.     

Nodal structure and stimulus relatedness in equivalence classes: post-class formation preference tests

Three experiments used postclass formation within-class preference test performances to evaluate the effects of nodal distance on the relatedness of stimuli in equivalence classes. In Experiment 1, two 2-node four-member equivalence classes were established using the simultaneous protocol in which all of the baseline relations were trained together, after which all emergent relations probes were presented together. All training and testing was done using match-to-sample trials that contained two comparisons. After class formation, the effects of nodal distance were evaluated using within-class preference tests that contained samples and both comparisons from the same class. These tests yielded inconsistent performances for most participants. Experiment 2 replicated Experiment 1, but a third null comparison was used on all trials during class formation. Thereafter, virtually all of the within-class probes, for all participants, evoked performances that were consistent with the predicted effects of nodal distance, that is, the selection of comparisons that were nodally closer to the samples. It appears, then, that the establishment of the equivalence classes with a third null comparison induced control by nodal structure of the classes. Experiment 3 demonstrated the generality of these findings with larger classes that contained more nodal separations, that is, three-node five-member classes. Emergent-relations tests conducted immediately after the within-class tests showed the classes to be intact. Thus, the differential relatedness of stimuli in a class or their interchangeability depended on the content of a test trial: within-class probes occasioned responding indicative of differential strength among the stimuli in the class, while cross-class tests occasioned responding indicative of interchangeability of stimuli in the same class.     

Generalization of cross-modal stimulus equivalence classes: operant processes as components in human category formation.

This study employed a stimulus-class rating procedure to explore whether stimulus equivalence and stimulus generalization can combine to promote the formation of open-ended categories incorporating cross-modal stimuli. A pretest of simple auditory discrimination indicated that subjects (college students) could discriminate among a range of tones used in the main study. Before beginning the main study, 10 subjects learned to use a rating procedure for categorizing sets of stimuli as class consistent or class inconsistent. After completing conditional discrimination training with new stimuli (shapes and tones), the subjects demonstrated the formation of cross-modal equivalence classes. Subsequently, the class-inclusion rating procedure was reinstituted, this time with cross-modal sets of stimuli drawn from the equivalence classes. On some occasions, the tones of the equivalence classes were replaced by novel tones. The probability that these novel sets would be rated as class consistent was generally a function of the auditory distance between the novel tone and the tone that was explicitly included in the equivalence class. These data extend prior work on generalization of equivalence classes, and support the role of operant processes in human category formation.     

The Way Evaluation Tastes: Tasting as an Embodied Cue of Evaluation

The current theory and research on embodiment have indicated that the basic bodily experiences, which may be more fundamental and important than previously suggested, can influence human cognitive processes. Drawing upon this perspective, the present study examined the hypothesis that the psychological experience of evaluation is grounded in the physical experience of tasting. In three experiments, we found that a tasting cue facilitated evaluation-related conceptual processing in a lexical decision task (Experiment 1), and induced a desire to evaluate toward novel stimuli (Experiment 2). Furthermore, sweet tastes were associated with more positive and secure evaluations than bitter tastes (Experiment 3). These findings provide converging evidence supporting the prediction that tasting as an embodied cue of evaluation.     

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.     

Nodal structure and the partitioning of equivalence classes

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.     

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.     

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 logarithmic transformation on estimating the parameters of the generalized matching law

This study examined stimulus class membership established via stimulus-reinforcer relations. Mentally retarded subjects learned conditional discriminations with four two-member sets of visual stimuli (A, B, C, and D). On arbitrary-matching trials, they selected comparison stimuli B1 and B2 conditionally upon samples A1 and A2, respectively, and C1 and C2 conditionally upon B1 and B2, respectively. On identity-matching trials, they selected all stimuli as comparisons conditionally upon identical stimuli as samples. Throughout training, correct selections of A1, B1, C1, and D1 were followed by one reinforcer, R1, and those of A2, B2, C2, and D2 were followed by another, R2. Subsequent tests documented the formation of two four-member stimulus classes, A1-B1-C1-D1 and A2-B2-C2-D2. The class membership of the A, B, and C stimuli could have been based on equivalence relations that resulted from the arbitrary-matching training. D1 and D2 had never appeared on arbitrary-matching trials, however. Their class membership must have been based on relations with R1 and R2, respectively. Results thus confirm a previous finding that stimulus classes can be expanded via stimulus-reinforcer relations. They also define more precisely the potential nature of those classes and the conditions under which class membership can be established.     

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.     

The role of common motor responses in stimulus categorization by preschool children

The purpose of this study was to assess the role of common motor responses as the "speaker" behavior on stimulus class formation, and the emergence of functional classes. Experiment 1 examined whether training one motor response to a set of three stimuli and a second motor response to another set of three stimuli would result in correct category-sort responses for 5 typically developing preschool children. Three of the children passed the categorization tests. Experiment 2 examined whether the classes formed in Experiment 1 were functional classes, and whether participants who did not pass categorization tests in Experiment 1 would do so following common vocal tact training. The 2 participants who failed categorization tests in Experiment 1 passed these tests in Experiment 2, although none of the participants passed the tests for functional classes. The results of the current study did not unequivocally support the naming hypothesis. Future research should therefore evaluate other possible sources of control that aid in stimulus categorization.     

Soames on Russell’s logic: a reply

In “What is History For?,” Scott Soames responds to criticisms of his treatment of Russell’s logic in volume 1 of his Philosophical Analysis in the Twentieth Century. This note rebuts two of Soames’s replies, showing that a first-order presentation of Russell’s logic does not fit the argument of the Introduction to Mathematical Philosophy, and that Soames’s contextual definition of classes does not match Russell’s contextual definition of classes. In consequence, Soames’s presentation of Russell’s logic misrepresents what Russell took to be its technical achievement and its philosophical significance.     

Six-member stimulus classes generated by conditional-discrimination procedures

In conditional-discrimination procedures with three sets of stimuli, A, B, and C, three stimuli per set (A1A2A3, B1B2B3, and C1C2C3), subjects (children and adults) learned to select Set-B and Set-C comparisons conditionally upon Set-A samples (A1B1, A1C1, A2B2, A2C2, A3B3, A3C3). If the conditional-discrimination procedures also generated equivalence relations, three 3-member stimulus classes would be demonstrable, A1B1C1, A2B2C2, and A3B3C3. In addition to these three sets, the present experiments used three other sets of stimuli--D, E, and F. The subjects learned to select Set-E and Set-F comparisons conditionally upon Set-D samples (D1E1, D1F1, D2E2, D2F2, D3E3, D3F3). This established a second group of three 3-member stimulus classes, D1E1F1, D2E2F2, and D3E3F3. In all, two groups of three 3-member classes were established by teaching subjects 12 conditional discriminations. The two groups of 3-member classes were then combined (successfully for 5 of 8 subjects) into a single group of three 6-member classes by teaching the subjects three more conditional relations (E1C1, E2C2, and E3C3). With three other children, enlarging the classes one member at a time also produced 6-member classes. As a consequence of class formation, 60 untrained conditional relations emerged from 15 that had been explicitly taught. Six of the subjects also proved capable of naming the stimuli consistently in accord with their class membership, but two subjects demonstrated class formation even in the absence of consistent naming.     

Equivalence class establishment, expansion, and modification in preschool children

Preschool children were taught four two-choice match-to-sample conditional discriminations with 10 arbitrary visual stimuli. For 6 participants, 2 of the 10 stimuli served as the sample, or conditional, stimuli in all discriminations. For 5 additional participants, the same pair of stimuli served as the discriminative, or comparison, stimuli in all discriminations. Equivalence classes were established with more participants in the latter group, replicating prior research with participants with retardation. Four participants, in whom equivalence classes were established and who were available for further participation, were exposed to new conditional discriminations without trial-by-trial feedback and involving some novel and some familiar stimuli. Consistent conditional responding was observed, and tests for inclusion of the novel stimuli in the original classes showed class expansion. Training to reverse the unreinforced conditional performances produced a reversal of class membership in 3 of 4 participants, an outcome not consistent with other studies. The results are discussed with respect to the interaction of class structure and size.     

The merger and development of equivalence classes by unreinforced conditional selection of comparison stimuli

Three experiments assessed the likelihood that subjects with histories of equivalence class development would respond conditionally on new discriminations in the absence of differential consequences for responses. In the first two experiments, two groups of subjects with different experimental histories, but whose performances showed four equivalence classes, responded on trials without explicit reinforcement involving samples from two of the classes and comparisons from the other two classes, in a two-choice matching-to-sample format. Subjects consistently selected a particular comparison in the presence of a particular sample. Subsequent tests showed the emergence of equivalence relations between stimuli from classes linked by the unreinforced conditional selections. Subsequently, in Experiment II, the subjects' responses in the conditional selection trials were reinforced if the selection was reversed from that made previously. Although reversed selection was maintained, 2 of the 3 subjects continued to perform on equivalence relation trials according to their original unreinforced selections. In the third experiment, these 2 subjects responded on a series of conditional discriminations involving three new pairs of sample stimuli and one new pair of comparison stimuli. No explicit reinforcement followed responses on any trial in this experiment. Subsequent tests for equivalence between sample stimuli revealed the development of two equivalence classes.     

Children's conceptions of physical events: Explicit and tacit understanding of horizontal motion

The conceptual understanding that children display when predicting physical events has been shown to be inferior to the understanding they display when recognizing whether events proceed naturally. This has often been attributed to differences between the explicit engagement with conceptual knowledge required for prediction and the tacit engagement that suffices for recognition, and contrasting theories have been formulated to characterize the differences. Focusing on a theory that emphasizes omission at the explicit level of conceptual elements that are tacitly understood, the paper reports two studies that attempt clarification. The studies are concerned with 6‐ to 10‐year‐old children's understanding of, respectively, the direction (141 children) and speed (132 children) of motion in a horizontal direction. Using computer‐presented billiards scenarios, the children predicted how balls would move (prediction task) and judged whether or not simulated motion was correct (recognition task). Results indicate that the conceptions underpinning prediction are sometimes interpretable as partial versions of the conceptions underpinning recognition, as the omission hypothesis would imply. However, there are also qualitative differences, which suggest partial dissociation between explicit and tacit understanding. It is suggested that a theoretical perspective that acknowledges this dissociation would provide the optimal framework for future research.