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

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.

Stimulus equivalence, generalization, and contextual stimulus control in verbal classes

Stimulus generalization and contextual control affect the development of equivalence classes. Experiment 1 demonstrated primary stimulus generalization from the members of trained equivalence classes. Adults were taught to match six spoken Icelandic nouns and corresponding printed words and pictures to one another in computerized three-choice matching-to-sample tasks. Tests confirmed that six equivalence classes had formed. Without further training, plural forms of the stimuli were presented in tests for all matching performances. All participants demonstrated virtually errorless performances. In Experiment 2, classifications of the nouns used in Experiment 1 were brought under contextual control. Three nouns were feminine and three were masculine. The match-to-sample training taught participants to select a comparison of the same number as the sample (i.e., singular or plural) in the presence of contextual stimulus A regardless of noun gender. Concurrently, in the presence of contextual stimulus B, participants were taught to select a comparison of the same gender as the sample (i.e., feminine or masculine), regardless of number. Generalization was assessed using a card-sorting test. All participants eventually sorted the cards correctly into gender and number stimulus classes. When printed words used in training were replaced by their picture equivalents, participants demonstrated almost errorless performances.

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.

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'.

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.

An evaluation of computer-based programmed instruction for promoting teachers' greetings of parents by name

Although greeting parents by name facilitates subsequent parent-teacher communication, baseline measures revealed that 4 preschool teachers never or rarely greeted parents by name during morning check-in. To promote frequent and accurate use of parents' names by teachers, the effects of a fully automated computerized assessment and programmed instruction (CAPI) intervention were evaluated in a multiple baseline design. The CAPI intervention involved assessment and training of relations among parents' and children's pictures and names, and produced rapid learning of parent names. The CAPI intervention also resulted in substantial improvements in the classroom use of parents' names for 3 of the 4 teachers; however, a supervisor-mediated feedback package (consisting of instructions, differential reinforcement, and error correction) was necessary to maintain name use for 2 of those teachers. The practical strengths and limitations of computer-based teacher training are discussed.

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.

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.

Stimulus generalization of behavioral history

Undergraduates responded under a variable-ratio 30 schedule in the presence of a 25-mm long line and on a differential-reinforcement-of-low-rate 6-s schedule when a 13-mm long line was present. Following this, a line-length continuum generalization test was administered under a fixed-interval 6-s schedule (Experiment 1) or extinction (Experiment 2). In both experiments, obtained generalization gradients conformed to typical postdiscrimination gradients. Responses were frequent under stimuli physically similar to the 25-mm line and infrequent under stimuli physically similar to the 13-mm line. The generalization gradients were generally asymmetric with peak response rates occurring at line lengths greater than 25 mm.

Naming and categorization in young children: vocal tact training

In three experiments, 2- to 4-year-old children, following pretraining with everyday objects, were presented with arbitrary stimuli of differing shapes. In Experiment 1A, 9 subjects were trained one common tact response, "zag," to three of these and a second tact, "vek," to another three. In category match-to-sample Test 1, 4 subjects sorted accurately when required only to look at the sample before selecting from five comparisons. The remaining 5 subjects succeeded in Test 2, in which they were required to tact the sample before selecting comparisons. Experiment 1B showed, for 2 of these subjects, that tact training with 12 arbitrary stimuli established two six-member classes that were still intact 6 weeks later. In Experiment 2, 3 new subjects participated in a common tact training procedure that ensured that none of the exemplars from the same class were presented together prior to the test for three-member classes. Two subjects passed category Test 1 and the third passed Test 2. Tests showed subjects' listener behavior in response to hearing /zog/ and /vek/ to be in place. These experiments indicate that common naming is effective in establishing arbitrary stimulus classes and that category match-to-sample testing provides a robust measure of categorization.

A new approach to the formation of equivalence classes in pigeons

Four pigeons were given simultaneous discrimination training with visual patterns arbitrarily divided into two sets, with the stimuli in one set designated A1, B1, C1, and D1 and those in the other set designated A2, B2, C2, and D2. In sequentially introduced training phases, the pigeons were exposed to a series of reversals to establish AB and then CD equivalences. In subsequent testing sessions, a subset of stimuli from one set served as positive stimuli and those from the other set as negative stimuli on training trials, and transfer of the reinforced relation to other members of the sets was tested with nonreinforced probe trials. The pigeons were trained further on AC and BD equivalences and then were tested for the emergence of untrained AD and BC equivalences. Two of the 4 pigeons exhibited the emergence of one of these untrained equivalences, evidence for the emergence of transitive relations. This finding suggests that the pigeons established three-member functional equivalence classes by incorporating separately trained multiple equivalence relations. Repeated reversal training and probe testing enabled us to explore the formation and expansion of functional equivalence classes in pigeons.

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.

Contextual control of stimulus generalization and stimulus equivalence in hierarchical categorization

The purpose of this study was to determine whether hierarchical categorization would result from a combination of contextually controlled conditional discrimination training, stimulus generalization, and stimulus equivalence. First, differential selection responses to a specific stimulus feature were brought under contextual control. This contextual control was hierarchical in that stimuli at the top of the hierarchy all evoked one response, whereas those at the bottom each evoked different responses. The evocative functions of these stimuli generalized in predictable ways along a dimension of physical similarity. Then, these functions were indirectly acquired by a set of nonsense syllables that were related via transitivity relations to the originally trained stimuli. These nonsense syllables effectively served as names for the different stimulus classes within each level of the hierarchy.

Naming and categorization in young children: vocal tact training

In three experiments, 2- to 4-year-old children, following pretraining with everyday objects, were presented with arbitrary stimuli of differing shapes. In Experiment 1A, 9 subjects were trained one common tact response, "zag," to three of these and a second tact, "vek," to another three. In category match-to-sample Test 1, 4 subjects sorted accurately when required only to look at the sample before selecting from five comparisons. The remaining 5 subjects succeeded in Test 2, in which they were required to tact the sample before selecting comparisons. Experiment 1B showed, for 2 of these subjects, that tact training with 12 arbitrary stimuli established two six-member classes that were still intact 6 weeks later. In Experiment 2, 3 new subjects participated in a common tact training procedure that ensured that none of the exemplars from the same class were presented together prior to the test for three-member classes. Two subjects passed category Test 1 and the third passed Test 2. Tests showed subjects' listener behavior in response to hearing /zog/ and /vek/ to be in place. These experiments indicate that common naming is effective in establishing arbitrary stimulus classes and that category match-to-sample testing provides a robust measure of categorization.

Perceptual classes established with forced-choice primary generalization tests and transfer of function

In Experiment 1, 20 college students learned two identity conditional discriminations using squares that differed in interior-fill percentage (called Fill23 and Fill77). A two-choice generalization test was then presented with number of test trials varied across groups of subjects. The test samples were 19 squares that ranged in fill value from 23% to 77%; the comparisons were squares with Fill23 and Fill77. The resulting gradients did not vary as a function of number of test trials. When the generalization test was repeated with a third comparison, "neither," the ranges of fill values that occasioned the exclusive selection of Fill23 or Fill77 were direct functions of the number of prior two-choice generalization trials. Finally, a disriminability test revealed that Fill23 and Fill77 were disciminable from the intermediate fill values. In Experiment 2, perceptual classes were established with 5 new students using 760 forced-choice generalization test trials. The student were then trained to select a different glyph in the presence of Fill23 and Fill77, followed by a three-choice generalization test in which the 19 fill stimuli served as samples and the two glyphs served as comparisons. The gradients ovelapped with those previously obtained during the three-choice generalization test that used Fill23 and Fill77 as comparisons. Finally, a discriminability test showed that many adjacent stimuli along thc fill dimension were discriminable from each other. Together, the results of both experiments suggest that ranges of fill-based stimuli functioned as members of perceptual classes, and each class also functioned as a transfer network for a new selection-based response.

Generalization and Transfer: An Interrelation of Paradigms and a Taxonomy of Knowledge Extension Processes

This article integrates work on generalization and transfer into a coherent framework. It analyzes the evolutionary problem with which generalization deals and then outlines a model of responses to a situation requiring generalization and a taxonomy of generalization and transfer processes. Key tenets are that many different generalization processes exist, that there are wide individual differences in which processes may occur, and that generalization of declarative knowledge usually involves concepts. Three experiments tested 2 tenets. One experiment suggested that generalization gradients found in the specialized paradigm used to study human stimulus generalization simply represent failure to perceptually discriminate between stimuli. The other experiments, involving a different paradigm, found step functions along dimensions instead of decremental gradients. They show that the traditional stimulus generalization paradigm is a type of concept learning paradigm. Participants generalize along a continuum by placing stimuli into categories. The experiments also show many different responses to a situation requiring generalization.

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.