Similarity- and nonsimilarity-based conceptualization in children and pigeons.

What is a concept? This question has interested philosophers and psychologists for centuries. Yet the diversity of opinion presently held by leading authorities on the matter shows how far we still are from satisfactorily answering this fundamental question.

Of special interest is the reformulation of the issue by two pioneers in behavior analysis: Fred S. Keller and William N. Schoenfeld. In their 1950 text, Principles of Psychology, Keller and Schoenfeld asserted that the very question--"What is a concept?"--is the wrong one to ask. Rather, we should ask, "What type of behavior is it that we call conceptual?" They suggested that "when a group of objects gets the same response, when they form a class the members of which are reacted to similarly, we speak of a concept". So, when a child is taught to respond "spoon" to different members of one class of objects and "bowl" to different members of another class of objects, we have observed conceptual behavior. Keller and Schoenfeld did not explicitly consider the transfer of discriminative responding to new stimuli. We assume that such transfer would be expected, so that new spoons and bowls would occasion appropriate behaviors, given that they did not differ too much in appearance from the training stimuli.

Keller and Schoenfeld saw no need for behavioral tools beyond the well-established principles of discrimination and generalization to explain conceptual behavior. "Generalization within classes and discrimination between classes--this is the essence of concepts".

Finally, Keller and Schoenfeld broke from tradition by proposing that conceptual behavior might very well be evidenced by nonverbal humans, like infants, and even by nonhuman animals. Given our own special interest in the matter, it is appropriate here to repeat Keller and Schoenfeld's (1950) insightful critique of the concept of "concept:"

It is curious to note the resistance that may be shown to the notion that the term concept need not be limited to matters capable of being verbalized or found only in the behavior of human adults. We seem to have here a problem in our own behavior. We have formed a concept of conceptual behavior which is based upon such factors as the age of the subject, his ability to verbalize, and the fact that he is human.

Of course, even those only faintly familiar with work in the area are aware that behavioral analyses, such as Keller and Schoenfeld's, have had rather little impact on mainstream research and theory in conceptualization. Cognitivists appear largely to have appropriated the study of concepts as their own.

One notable area of behavioristic study concerns the conceptual behavior of nonhuman animals. The primary impetus for this line of inquiry was the innovative research of Herrnstein and his collaborators on discriminations involving photographic stimuli (for a review of this research, see Herrnstein, 1985). This work, begun in 1964 by Herrnstein and Loveland, clearly established that pigeons could discriminate slides which portrayed a particular class of stimuli (like people, fish, or trees) from otherwise comparable slides which did not. Such discriminations not only held for large sets of previously seen slides, but they also generalized to novel slides from the feature-present and feature-absent categories. Successful stimulus generalization here confirms Herrnstein's contention that basic-level categories are open-ended; they comprise infinite examples of related stimuli.

When we began to research conceptual behavior in animals, we wished to build on the groundwork laid by Herrnstein. Thus, we used pigeons and taught them to discriminate photographic images. However, we wanted them to engage in a closer approximation to human conceptual behavior than the feature-present vs. feature-absent discriminations of Herrnstein's group. We thus required pigeons concurrently to discriminate slides depicting stimuli from four different classes of objects. Also, Herrnstein had reported difficulty in training pigeons to discriminate slides with humanmade objects from slides without those

objects. Thus, two of the four classes of stimuli we used involved natural objects and two involved humanmade objects.

Similarity-Based Conceptualization

Four-Category Discrimination and Generalization in Pigeons

We often teach and learn concepts by means of the "name" game. Here, for example, a parent opens a book, points to one of its illustrations, and asks the child, "What is it?" If the child makes the correct verbal response, then positive social reinforcement is provided. If the child makes the incorrect response, then no positive reinforcement is provided; instead, the parent may ask the child to try again; and, if this request also fails to occasion the correct response, then the parent may have to supply it. The "name" game is far from a diversion: It is the very deliberate and selective application of social reinforcement, so that different classes of discriminative stimuli gain control over the child's ever-expanding repertoire of verbal behavior.

We (Bhatt, Wasserman, Reynolds, & Knauss, 1988) tried to apply the gist of the "name" game to four pigeons, to see if they could concurrently report stimuli from four different categories of objects. Instead of requesting verbal behavior from our subjects, we asked the birds to report members of four different categories--cats, flowers, cars, and chairs--by pecking four circular keys surrounding a square central viewing screen. Each day, 40 color slides were shown depicting 10 discriminatively different examples from each of the four categories. After 30 pecks to the viewing screen to ensure that the slide was observed, the four report keys were illuminated, each with a different color. A single choice response was permitted. If it was to the correct key for reporting members of the category of stimulus shown on the viewing screen on that trial, then the pigeon was given food reinforcement; if it was to any of the three incorrect keys, then no reinforcement was given and a correction trial immediately followed. Pigeons continued to the next trial only after a correct choice. A pigeon might have to peck the top left key in response to pictures of cats, the top right key in response to pictures of flowers, the bottom left key in response to pictures of cars, and the bottom right key in response to pictures of chairs. Different pigeons received different category-key assignments, so that across subjects each key was equally often associated with each of the four categories.

Acquisition of discriminative responding was quite regular and rose from the chance score of 25% to about 80% correct after 30 days of training (Bhatt et al., 1988, Experiment 1 B). At no point in this experiment nor in many others conducted in our laboratory was there any sign that the pigeons categorized the humanmade stimuli more slowly or less accurately than they categorized the natural stimuli. Right after reaching 80%, the pigeons were given generalization testing with 10 new snapshots of objects in each of the four categories. The testing phase lasted 2 days, on each of which the pigeons saw 20 old slides and 20 new ones. Accuracy to the old slides averaged 81% and to the new ones 64% (a level significantly above the chance score of 25%). It is noteworthy that categorization accuracy was a bit lower to the novel test stimuli than it was to the familiar training stimuli. This generalization decrement may be explained by many theories of conceptual behavior: from exemplar models to prototype models (Smith & Medin, 1981; also see Astley & Wasserman, 1992). At the very least, this fact suggests that the pigeons had memorized some or all of the stimuli that they had seen during training.

The pigeons thus had acquired discriminative behavior which enabled them to categorize a set of highly complex stimuli that they had seen 30 times before and still other stimuli that they had never seen before. If, as Keller and Schoenfeld had argued, generalization within categories and discrimination between categories is the essence of concepts, then surely our pigeons can be said to have demonstrated conceptual behavior.

Later work further studied the categorization of old and new stimuli. First, Bhatt (1988, Experiment 1) found that accuracy to new stimuli was a direct function of the number of examples shown in each category during training: Accuracy to 8 new stimuli from each of four categories rose from 27% to 45% when the number of examples per category during training was increased from 1 to 4 and it rose from 45% to 63% when the number of examples per category was increased from 4 to 12. Second, pigeons came to respond discriminatively to stimuli from four different categories, even if individual examples were never repeated: Accuracy rose to 70% after 50 days of training, in which each day involved 10 novel instances from the categories people, flowers, cars, and chairs (Bhatt et al., 1988, Experiment 3). The fact that acquisition was supported by this procedure, in which each trial was both a training trial and a testing trial, clearly indicates that stimulus repetition is unnecessary for the acquisition of conceptual behavior. Finally, although unnecessary for conceptualization, stimulus repetition does hasten the process. Using an alternating-day procedure, Bhatt et al. (1988, Experiment 4) found that, although acquisition was clear in each case, discriminative performance rose more rapidly and reached higher levels on odd-numbered days (which involved the same repeating set of 40 slide stimuli) than on even-numbered days (which involved 40 new and never-repeating stimuli).

Concordance of Concepts in People and Pigeons

Another project explored a further implication of Keller and Schoenfeld's analysis: Conceptual categories entail collections of stimuli which are more similar to one another than they are to stimuli in other categories. It seems quite reasonable to hypothesize that many human conceptual categories do indeed comprise highly similar stimuli; such similarity can then be seen to be an important factor responsible for the emergence of the very concepts we are considering.

Imagine that a total slide pool comprises 80 items: 20 cats, 20 flowers, 20 cars, and 20 chairs. Now, suppose that to pigeons all 80 slides are equivalently similar to one another. If this supposition were true, then a group of pigeons trained to classify the stimuli into human conceptual categories should learn this task no faster than another group of pigeons trained to classify the same stimuli into completely arbitrary assortments, in which equal numbers of cats, flowers, cars, and chairs are associated with each of the four report responses. However, if to pigeons, members of each of the human conceptual categories more closely resemble one another than they resemble members of the other categories, then pigeons should learn the true categorization task far faster than they learn the pseudocategorization task. This prediction follows from the idea that correct responding in the true categorization task should be encouraged both by direct strengthening of responding to a particular key in the presence of a particular stimulus and by indirect strengthening attributable to similar stimuli in the same conceptual category occasioning the same response. In contrast, in the pseudocategorization task, correct responding should be encouraged only by direct strengthening of responding to a particular key in the presence of a particular stimulus; greater stimulus generalization within than between human conceptual categories here should equilibrate the likelihood of pecks to all four report keys, thus decreasing the accuracy of performance.

When we (Wasserman, Kiedinger, & Bhatt, 1988, Experiment 2) administered these procedures to two groups of four pigeons each, the results were unequivocal: True categorization subjects acquired discriminative responding faster and reached higher levels of accuracy than did pseudocategorization subjects. Mean accuracy in the true category group exceeded 50% by 20 days of training (40 trials per day) and it exceeded 75% by 40 days of training; mean accuracy in the pseudocategory group failed to surpass 50% in 40 days of training. lt would thus be fair to conclude that, even to pigeons, members of a human conceptual category resemble one another more than they resemble members of different conceptual categories.

More direct evidence on the perceived similarity of category members comes from a study (Astley & Wasserman, 1992, Experiment 2) in which pigeons learned a go/no go discrimination with a set of 60 different slides: 12 S+s and 48 S-s. All birds saw the same set of S-s: 12 people, 12 flowers, 12 cars, and 12 chairs. Different birds had different S+s: a bird's S+s might be 12 people, 12 flowers, 12 cars, or 12 chairs. Assuming that the 12 S+s are equally similar to all 48 S-s, responses should be randomly distributed among the four S- categories, including the one from which the S+s were picked. However, if to pigeons, members of a given human conceptual category more closely resemble one another than they resemble members of different conceptual categories, then responses should be nonrandomly distributed and should be made disproportionately to the S-s from the same category as the S+s.

Precisely the latter result was obtained regardless of whether the S+s involved pictures of people, flowers, cars, or chairs. Over all 16 days of multiple schedule training and all 8 pigeons, 43% (rather than 25%) of all S- responses were made to stimuli from the S+ category. This research thus discloses that pigeons group similar stimuli together, even when such grouping is unrelated to the prevailing contingencies of reinforcement. Unlike our earlier studies which first explicitly provided pigeons with reinforcement for making correct categorization responses and then found generalization to untrained instances, categorical generalization here was evidenced by the birds' untrained propensity to respond most to negative discriminative stimuli from the same conceptual category as the positive discriminative stimuli. There were surely no differential reinforcers in place for responses to any of the S-s, whether those stimuli were from the same or from a different category as the S+s.

Generalization and Conceptualization

Given our data on conceptual generalization, one might ask whether the differential reinforcement we assiduously administered in our first experiments really created the conceptual behavior shown by our pigeons. This may seem a strange question to ask, but Herrnstein and de Villiers (1980) speculated that differential reinforcement may not produce, but simply disclose extant concepts: "Something in the pigeon's perceptual dynamics ties |stimuli~ together as a class, prior to differential reinforcement". This argument is tantamount to saying that primary stimulus generalization or perceptual similarity is the root of conceptual behavior.

Some theorists have questioned the completeness of this account. Lea (1984) proposed that a true concept comprises stimuli that are tied together by relations that are not based solely on perceptual similarity. He argued that if responses learned to some members of a category transfer to others and if such transfer is based only on perceptual similarity, then the very idea of a concept is superfluous; primary stimulus generalization alone can completely explain transfer from some category members to others.

If we accept Lea's proposal that concepts entail collections of stimuli whose coherence represents something more than perceptual similarity, then just what is that "something more" that allows the aggregation of perceptually dissimilar stimuli? One possibility is that stimuli which are simply associated with the same response or context will come to be classed together, despite their perceptual dissimilarity. As an example, because of a common response (beds and lamps are both called "furniture") and a common context (beds and lamps are usually sold in furniture stores), perceptually different stimuli (beds and lamps) come to be grouped into a common class or concept (furniture). Such perceptually heterogeneous collections are quite familiar and are termed superordinate categories by Rosch and Mervis (1975).

Importantly, the limits of a similarity-based approach to concepts were noted by Keller and Schoenfeld (1950), whose behavioral analysis has been the theoretical centerpiece of this paper. They argued that secondary or mediated generalization may play a large role in human conceptual behavior. Such secondary or mediated generalization is said to occur when perceptually different stimuli like the words "urn" and "vase" are associated with a common set of objects, thereby making one verbal stimulus the functional equivalent of another. According to Keller and Schoenfeld, "Generalizations are said to be mediated when they are based upon a stimulus equivalence which results from training".

Just what training supports stimulus equivalence? Keller and Schoenfeld were not specific. They say: "Classes of objects or events, differently responded to, develop different concepts". So, different stimuli associated with the same contingencies of reinforcement should presumably become functional equivalents of one another. Although they discuss functional stimulus equivalence in the context of human verbal behavior, there is no reason why Keller and Schoenfeld should limit nonsimilarity-based conceptualization to human adults.

Nonsimilarity-Based Conceptualization

Evidence from Animal Behavior

If we grant that adult human conceptual behavior may involve nonsimilarity-based transfer via secondary or mediated generalization, then we must ask whether there is any support for the possibility that animals exhibit nonsimilarity-based conceptualization (for early negative evidence, see Bhatt & Wasserman, 1989). In one of the clearest cases to date, Vaughan (1988) found that, after many discrimination reversals, pigeons came to treat members of each of two 20-item slide sets as functional equivalents of one another. Importantly, all 40 slides depicted trees; thus, the 20 items in each set were random assortments, with no obvious perceptual "glue" to bind them together into two classes entailing greater intraclass than interclass similarity. Other evidence of learned stimulus equivalence in pigeons was reported by Urcuioli, Zentall, Jackson-Smith, and Steirn (1989) and by Zentall, Steirn, Sherburne, and Urcuioli (1991).

We (Wasserman, DeVolder, & Coppage, 1992) recently completed a project addressing the issue of superordinate conceptualization in pigeons using the procedure outlined in Table 1. This procedure entailed three steps. First, pigeons were trained to classify 12 different stimuli from each of four basic-level categories (people, flowers, cars, and chairs) into two arbitrary aggregations. (To control for the effects of intraclass similarity, half of the subjects received as C1, C2, C3, and C4, respectively, slides of flowers, chairs, cars, and people, and the other half received as C1, C2, C3, and C4, respectively, slides of people, flowers, chairs, and cars.) To this end, Response 1 was reinforced in the presence of members of Category 1 and members of Category 2, whereas Response 2 was reinforced in the presence of members of Category 3 and members of Category 4. It is during this step of training that members of Categories 1 and 2 and members of Categories 3 and 4 might come to be merged into two classes of functionally equivalent, but perceptually different, stimuli. Second, pigeons were trained to make new responses to members of Categories 1 and 3 only, with Response 3 being correct to members of Category 1 and Response 4 being correct TABULAR DATA OMITTED to members of Category 3. (To control for horizontal vs. vertical reassignment of report keys from the original training locations, half of the subjects in each stimulus assignment subgroup received horizontal reassignment of R3 to C1 and R4 to C3 and half received vertical reassignment). Although only stimuli from Categories 1 and 3 were reassigned to new responses during this second step of training, stimuli from Categories 2 and 4 might also have been affected if the training in the first step were effective in establishing stimuli from Categories 1 and 2 as one aggregate group and stimuli from Categories 3 and 4 as a second aggregate group. The third and final step tested the pigeons for their tendency to make Response 3 vs. Response 4 to stimuli from Categories 2 and 4, the two classes of stimuli withheld from the second step of training. Even though never before taught to make Response 3 or Response 4 to stimuli from Categories 2 or 4, the clear expectation from combined category formation in the first step would be that birds should predominately make Response 3 to stimuli from Category 2 and Response 4 to stimuli from Category 4. Table 2 shows all of the stimulus and response assignments that were given during all three steps of the training procedure in this experiment.

Table 2
Stimulus and Response Assignments for Individual Subjects

Assignment   C1   C2   C3   C4   R1   R2   R3   R4

     1       Fl   Ch   Ca   Pe   TR   BL   TL   BR
     2       Fl   Ch   Ca   Pe   TR   BL   BR   TL
     3       Pe   Fl   Ch   Ca   TR   BL   TL   BR
     4       Pe   Fl   Ch   Ca   TR   BL   BR   TL

Note. C1, C2, C3, and C4 represent the four classes of
photographic stimuli with 12 snapshots in each class; R1, R2,
R3, and R4 represent the four different report responses which
were afforded to the subjects; Fl, Pe, Ch, and Ca refer,
respectively, to the classes flowers, people, chairs, and cars;
and, TL, TR, BL, and BR, refer, respectively, to the top-left,
top-right, bottom-left, and bottom-right report responses. Each
of the four different assignments was given to two pigeons and
to five preschool children.

Because a complete account of the study is available (Wasserman et al., 1992), we will concentrate here on the final phases when discriminative responding was strongest. In the last four-session block of Original Training, the mean percentage of correct choice responses was 89%. In the last four-session block of Reassignment Training, the mean percentage of correct choice responses was 89%. Across all four sessions of Testing, the mean percentage of correct choice responses to reassigned stimuli (C1 and C3) was 87% and to nonreassigned stimuli (C2 and C4) it was 72%. For both reassigned and nonreassigned stimuli on each test session, obtained accuracy significantly exceeded chance accuracy by binomial test. Finally, as to individual subject performance, across all four test sessions, the accuracy of all eight birds to the reassigned stimuli significantly exceeded the chance accuracy score of 50%; the accuracy of six of the eight birds to the nonreassigned stimuli did so.

The present three-step procedure therefore proved highly effective in producing and disclosing nonsimilarity-based conceptualization in pigeons. Merely by being associated with a common response in the first step, classes of perceptually dissimilar stimuli, like cars and chairs, appear to amalgamate into a new category of functionally equivalent stimuli. Thus, requiring a new response to be performed to only one of these two stimulus classes in the second step now brings about transfer to the other stimulus class in the third step.

Evidence from Preschool Children's Behavior

We were both pleased and surprised by the magnitude and robustness of our pigeons' nonsimilarity-based conceptual behavior. But, without a basis of comparison, we were unsure of how pleased and surprised to be. Therefore, we undertook a parallel project with preschool children given a photograph-sorting task to assess the generality of our results with pigeons. This project followed exactly the same logic and plan as the pigeon project.

The subjects were 20 children recruited from a preschool in a large Midwestern community. The children's ages ranged from 4 yr, 5 mo to 5 yr, 10 mo, with a mean age of 4 yr, 10 mo. Half of the children were boys and half were girls. The children were compensated for their participation with a $1.00 gift certificate at a local ice cream parlor.

A large white poster board laminated in clear acrylic to prevent soiling served as the response board. There were four rectangles outlined in each quadrant of the board and one rectangle located centrally. During each phase of the experiment, two diagonal rectangles were occluded by large Xs, rendering them unavailable. The same 48 snapshots employed in the pigeon experiment were used here. These photographs were laminated in clear acrylic to prevent damage caused by handling by the experimenter and the children.

There were three phases in the study. In the first phase, Original Training, children received a total of 48 trials. On each trial, the experimenter placed a photograph in the center rectangle and asked the child to place it in the correct choice location. During this phase, the top left and bottom right locations were occluded, leaving only the top right and bottom left rectangles available as choice responses. Correct responses were verbally reinforced ("that is correct") and incorrect responses were verbally punished ("that is incorrect"); no correction trials were given here or in any of the two following phases. Stimulus and response assignments followed the same plan used in the pigeon project. Original Training involved photographs from C1, C2, C3, and C4, and continued for 48 trials for all children; by this time, each child had reached the 90% correct level during at least one 12-trial training block.

Immediately following Original Training, each child underwent Reassignment Training during which the top right and bottom left response locations were occluded, leaving only the top left and bottom right locations available as choice responses. Reassignment Training utilized only two of the stimulus classes (C1 and C3) from Original Training and comprised a total of 24 trials; by this time, each child had reached the 90% correct level during at least one 12-trial training block.

After completion of Reassignment Training, each child was shown all of the 48 photographs one time each during a single Testing period. As in Reassignment Training, only the top left and bottom right rectangles were available as choice responses. As in the two prior phases, differential reinforcement was given for trials involving photographs from C1 and C3. Nondifferential positive reinforcement ("that is correct") was given for trials involving photographs from C2 and C4. During Testing, the mean percentage of correct choice responses to reassigned stimuli (C1 and C3) was 99% and to nonreassigned stimuli (C2 and C4) it was 80%. For both reassigned and nonreassigned stimuli, obtained accuracy significantly exceeded chance accuracy by binomial test. As to individual subject performance, Table 3 shows that the accuracy of all 20 children to the reassigned stimuli significantly exceeded the chance accuracy score of 50%; the accuracy of 13 of the 20 children to the nonreassigned stimuli did so.

TABULAR DATA OMITTED

Compared with the performance of our pigeons, our children mastered the tasks faster and reached higher levels of discriminative behavior; nevertheless, their behavior to reassigned and nonreassigned stimuli in testing was rather similar. Mean first-session accuracy of pigeons and children to reassigned stimuli was 88% and 99%, respectively; mean first-session accuracy of pigeons and children to nonreassigned stimuli was 78% and 80%, respectively. Of both the pigeons and the children, 100% responded significantly above chance levels to the reassigned stimuli; 75% of the pigeons and 65% of the children responded significantly above chance levels to the nonreassigned stimuli. In each case, the evidence was clear that association with a common response was sufficient for stimuli from perceptually different classes to join into a single class of functionally equivalent stimuli. Because of the design of the experiments, the transfer of training from reassigned to nonreassigned stimuli seems best interpreted as representing nonsimilarity-based conceptualization.

Concluding Comments

"|E~quivalent stimuli is what we mean when we speak of a concept". These words of Keller and Schoenfeld locate the study of concepts squarely within the experimental analysis of behavior. Nevertheless, the research discussed in this paper makes it clear that the origins of stimulus equivalence may be quite different. On the one hand, stimulus equivalence may result from the perceived similarity of stimuli. In this case, primary stimulus generalization may be said to support the transfer of discriminative responding from some stimuli to others. On the other hand, stimulus equivalence may result from prior experience. In this case, secondary or mediated stimulus generalization may be said to support the transfer of discriminative responding from some stimuli to others. From this vantage point, although differential contingencies of reinforcement may be necessary to disclose conceptual behavior, such contingencies may not be necessary to produce it. Pigeons and children alike are capable of similarity-based and nonsimilarity-based conceptualization; but, in the case of similarity-based conceptual behavior differential reinforcement appears to disclose preexisting concepts, whereas in the case of nonsimilarity-based conceptual behavior it appears to produce new ones.

Mediational Accounts of Nonsimilarity-Based Conceptualization

Our success in demonstrating nonsimilarity-based conceptualization in pigeons and children brings us to the difficult matter of the nature of the behavioral processes involved in such mediated transfer. On the face of it, there is good reason to point to the importance of the common behavior that was performed to members of the conjoint categories. Thus, R1 was the common response to members of both C1 and C2. Even though unavailable during reassignment training when R3 was required to members of C1, the incipient performance of that initial response and the feedback thereby produced by it could have become part of the complex of discriminative stimuli associated with R3. Later presentation of members of C2, even though never before paired with R3, could have effectively led to the performance of R3 because these stimuli were associated with part of the discriminative stimulus complex associated with R3.

A second possibility is undoubtedly more plausible for our children than for our pigeons. Here, one might imagine that, when the same response is required of stimuli from two basic-level categories like flowers and chairs, presentation of stimuli from either category elicits a common covert response like a flower resting on a chair. Whereas the theoretics behind the first mediational approach are traceable to the fractional anticipatory responses of Hull and Spence (also see Osgood, 1953), the second mediational notion is decidedly more cognitive and its testable implications are not so readily apparent. We look forward to exploring these and other mediational interpretations in future research with pigeons and preschool children.

On the Terminology of Emergent Stimulus Control 

Keller and Schoenfeld considered stimulus equivalence to be central to conceptual behavior. Our own research on nonsimilarity-based conceptualization in pigeons and children used an experimental design which demonstrated that stimuli from one stimulus class could be effectively substituted for stimuli from another perceptually different stimulus class. This transfer of stimulus control can be said to be emergent because discriminative responding to one of the two classes of stimuli occurs without any explicit reinforcement of such responding. Because the establishing operation of this emergent stimulus control was the association of the two classes of stimuli with the same response, we use the terms "learned" and "functional" stimulus equivalence to refer to the stimulus control we observed to the nonreassigned stimuli during the test phase of our experiments.

Of course, a burgeoning area of research was begun by Sidman on stimulus equivalence in conditional discrimination situations rather unlike the one studied here. A mathematically derived definition of stimulus equivalence has sprung from that work which is of a highly precise and confined form (Sidman & Tailby, 1982). We make no claim that the procedures we have used in our own research would guarantee that our human and animal subjects would pass the specific tests of symmetry, reflexivity, and transitivity; indeed, we are not sure whether all of these tests make sense outside of matching-to-sample procedures. We do believe that the learned equivalence of stimuli is an important and underinvestigated realm of experimental inquiry, and that any efforts to constrain the recent upsurge of interest in the area by arbitrary definitional criteria would be counterproductive to a behavioral understanding of this exciting domain of cognition (for more on this matter, see Saunders & Green, 1992).

References

ASTLEY, S. L., & WASSERMAN, E. A. (1992). Categorical discrimination and generalization in pigeons: All negative stimuli are not created equal. Journal of Experimental Psychology: Animal Behavior Processes, 18, 193-207.

BHATT, R. S. (1988). Categorization in pigeons: Effects of category size. congruity with human categories, selective attention, and secondary generalization. Unpublished doctoral dissertation, University of Iowa, Iowa City.

BHATT, R. S., & WASSERMAN, E. A. (1989). Secondary generalization and categorization in pigeons. Journal of the Experimental Analysis of Behavior, 52, 213-224.

BHATT, R. S., WASSERMAN, E. A., REYNOLDS, W. F., JR., & KNAUSS, K. S. (1988). Conceptual behavior in pigeons: Categorization of both familiar and novel examples from four classes of natural and artificial stimuli. Journal of Experimental Psychology: Animal Behavior Processes, 14, 219-234.

HERRNSTEIN, R. J. (1985). Riddles of natural categorization. Philosophical Transactions of the Royal Society, B308, 129-144.

HERRNSTEIN, R. J., & DE VILLIERS, P. A. (1980). Fish as natural category for people and pigeons. In G. Bower (Ed.), The psychology of learning and motivation (pp. 59-95). San Diego, CA: Academic Press.

HERRNSTEIN, R. J., & LOVELAND, D. H. (1964). Complex visual concept in the pigeon. Science, 146, 549-551.

KELLER, F. S., & SCHOENFELD, W. N. (1950). Principles of psychology. New York: Appleton-Century-Crofts.

LEA, S. E. G. (1984). In what sense do pigeons learn concepts? In H. L. Roitblat, T. G. Bever, & H. S. Terrace (Eds.), Animal cognition. Hillsdale, NJ: Erlbaum.

OSGOOD, C. E. (1953). Method and theory in experimental psychology. New York: Oxford University Press.

ROSCH, E., & MERVIS, C. B. (1975). Family resemblances: Studies in the internal structure of categories. Cognitive Psychology. 7, 573-605.

SAUNDERS, R. P., & GREEN, G. (1992). The nonequivalence of behavioral and mathematical equivalence. Journal of the Experimental Analysis of Behavior, 57, 227-241.

SIDMAN, M., & TAILBY, W. (1982). Conditional discrimination vs. matching to sample: An expansion of the testing paradigm. Journal of the Experimental Analysis of Behavior, 37, 5-22.

SMITH, E. E., & MEDIN, D. L. (1981). Categories and concepts. Cambridge, MA: Harvard University Press.

URCUIOLI, P. J., ZENTALL, T. R., JACKSON-SMITH, P., & STEIRN, J. N. (1989). Evidence for common coding in many-to-one matching: Retention, intertrial interference, and transfer. Journal of Experimental Psychology: Animal Behavior Processes, 15, 264-273.

VAUGHAN, W., JR. (1988). Formation of equivalence sets in pigeons. Journal of Experimental Psychology: Animal Behavior Processes, 14, 36-42.

WASSERMAN, E. A., DEVOLDER, C. L., & COPPAGE, D. J. (1992). Nonsimilarity-based conceptualization in pigeons. Psychological Science, 3, 374-379.

WASSERMAN, E. A., KIEDINGER, R. E., & BHATT, R. S. (1988). Conceptual behavior in pigeons: Categories, subcategories, and pseudocategories. Journal of Experimental Psychology: Animal Behavior Processes, 14, 235-246.

ZENTALL, T. R., STEIRN, J. N., SHERBURNE, L. M., & URCUIOLI, P.J. (1991). Common coding in pigeons assessed through partial versus total reversals of many-to-one conditional and simple discriminations. Journal of Experimental Psychology: Animal Behavior Processes, 17, 194-201.