Emergent identity matching after successive matching training. II: Reflexivity or transitivity

Three experiments evaluated whether the apparent reflexivity effect reported by Sweeney and Urcuioli (2010) for pigeons might, in fact, be transitivity. In Experiment 1, pigeons learned symmetrically reinforced hue-form (A-B) and form-hue (B-A) successive matching. Those also trained on form-form (B-B) matching responded more to hue comparisons that matched their preceding samples on subsequent hue-hue (A-A) probe trials. By contrast, most pigeons trained on just A-B and B-A matching did not show this effect; but some did--a finding consistent with transitivity. Experiment 2 showed that the latter pigeons also responded more to form comparisons that matched their preceding samples on form-form (B-B) probe trials. Experiment 3 tested the prediction that hue-hue matching versus hue-hue oddity, respectively, should emerge after symmetrically versus asymmetrically reinforced arbitrary matching relations if those relations are truly transitive. For the few pigeons showing an emergent effect, comparison response rates were higher when a probe-trial comparison matched its preceding sample independently of the baseline contingencies. These results indicate neither a reflexivity nor a transitivity effect but, rather, a possible identity bias.     

Reflexivity without identity matching training: A first demonstration

Until now, the equivalence property of reflexivity—matching physically identical stimuli to themselves after training on a set of arbitrary matching relations—has not been demonstrated in any animal, human or nonhuman. Previous reports of reflexivity have either implicitly or explicitly involved reinforced training on other identity matching relations. Here we demonstrate reflexivity without prior identity matching training. Pigeons received concurrent successive matching training on three arbitrary matching tasks: AB (hue–form), BC (form–hue), and AC (hue–hue with different hues in the A and C sets). Afterwards, pigeons were tested for BB (form–form) reflexivity. Consistent with the predictions of Urcuioli's ( 2008 ) theory, pigeons preferentially responded to B comparison stimuli that matched the preceding B sample stimuli in testing (i.e., BB reflexivity). A separate experiment showed that a slightly different set of arbitrary matching baseline relations yielded a theoretically predicted “anti‐reflexivity” (or emergent oddity) effect in two of five pigeons. Finally, training on just two arbitrary successive matching tasks (AB and BC) did not yield any differential BB responding in testing for five of eight pigeons, with two others showing reflexivity and one showing antireflexivity. These data complement previous findings of symmetry and transitivity (the two other properties of equivalence) in pigeons.     

Reflexivity in pigeons

A recent theory of pigeons' equivalence-class formation (Urcuioli, 2008) predicts that reflexivity, an untrained ability to match a stimulus to itself, should be observed after training on two "mirror-image" symbolic successive matching tasks plus identity successive matching using some of the symbolic matching stimuli. One group of pigeons was trained in this fashion; a second group was trained similarly but with successive oddity (rather than identity). Subsequently, comparison-response rates on novel matching versus mismatching sequences with the remaining symbolic matching stimuli were measured on nonreinforced probe trials. Higher rates were observed on matching than on mismatching probes in the former group. The opposite effect--higher rates on mismatching than matching probes--was mostly absent in the latter group, despite being predicted by the theory. Nevertheless, the ostensible reflexivity effect observed in former group may be the first time this phenomenon has been demonstrated in any animal.     

Associative symmetry in the pigeon after successive matching-to-sample training

If an organism is explicitly taught an A→B association, then might it also spontaneously learn the symmetrical B→A association? Little evidence attests to such “associative symmetry” in nonhuman animals. We report for the first time a clear case of associative symmetry in the pigeon. Experiment 1 used a successive go/no go matching‐to‐sample procedure, which showed all of the training and testing stimuli in one location and intermixed arbitrary and identity matching trials. We found symmetrical responding that was as robust during testing (B→A) as during training (A→B). In Experiment 2, we trained different pigeons using only arbitrary matching trials before symmetry testing. No symmetrical responding was found. In Experiment 3, we trained other pigeons with only arbitrary matching trials and then tested for symmetry. When these pigeons, too, did not exhibit symmetrical responding, we retrained them with intermixed identity and arbitrary matching trials. Less robust symmetrical responding was obtained here than in Experiment 1. Collectively, these results suggest that identity matching may have to be learned concurrently with arbitrary matching from the outset of training for symmetry to emerge.     

ASSOCIATIVE SYMMETRY,ANTISYMMETRY, AND A THEORY OF PIGEONS' EQUIVALENCE‐CLASS FORMATION

Five experiments assessed associative symmetry in pigeons. In Experiments 1A, 1B and 2, pigeons learned two‐alternative symbolic matching with identical sample‐ and comparison‐response requirements and with matching stimuli appearing in all possible locations. Despite controlling for the nature of the functional stimuli and insuring all requisite discriminations, there was little or no evidence for symmetry. By contrast, Experiment 3 demonstrated symmetry in successive (go/no‐go) matching, replicating the findings of Frank and Wasserman (2005). In view of these results, I propose that in successive matching, (1) the functional stimuli are stimulus‐temporal location compounds, (2) continual nonreinforcement of some sample‐comparison combinations juxtaposed with reinforcement of other combinations throughout training facilitates stimulus class formation, (3) classes consist of the elements of the reinforced combinations, and (4) common elements produce class merger. The theory predicts that particular sets of training relations should yield “antisymmetry”: Pigeons should respond more to a reversal of the nonreinforced symbolic baseline relations than to a reversal of the reinforced relations. Experiment 4 confirmed this counterintuitive prediction. These results and other theoretical implications support the idea that equivalence relations are a natural consequence of reinforcement contingencies.     

Choice, experience, and the generalized matching law

Five pigeons were exposed to different pairs of concurrent variable-interval, variable-interval schedules on nine experimental conditions of 30 sessions each. For every session, the parameters of the generalized matching equation were computed for the first five, six, seven, eight, and nine experimental conditions. The exponent a, both for response and time distribution, tended to decrease with increases in number of experimental conditions and to increase with number of sessions per condition, but values of k (bias) varied unsystematically. When the subjects were exposed to five new pairs of schedules, with 55 sessions per condition, the findings were confirmed. Data from the literature on the generalized matching law suggest that the variability of exponent values may be explained in part by the use of naive or experienced subjects in different investigations and by the variability in number of experimental conditions and in number of sessions per condition.     

A REPLICATION AND EXTENSION OF THE ANTISYMMETRY EFFECT IN PIGEONS

Pigeons trained on successive AB symbolic matching show emergent BA antisymmetry if they are also trained on successive AA oddity and BB identity ( Urcuioli, 2008 , Experiment 4). In other words, when tested on BA probe trials following training, they respond more to the comparisons on the reverse of the nonreinforced AB baseline trials than on the reverse of the reinforced AB baseline trials (the opposite of an associative symmetry pattern). The present experiment replicated this finding. In addition, it showed that antisymmetry also emerged after baseline training on successive AB symbolic matching, AA identity, and BB oddity, consistent with the prediction from Urcuioli's (2008) theory of pigeons' stimulus‐class formation. Together, these results provide further empirical support for that theory including the proposition that the functional stimuli in pigeons' successive matching consist of the nominal stimuli plus their ordinal positions within a trial.     

Associative symmetry by pigeons after few-exemplar training

The present experiment investigated whether pigeons can show associative symmetry on a two-alternative matching-to-sample procedure. The procedure consisted of a within-subject sequence of training and testing with reinforcement, and it provided (a) exemplars of symmetrical responding, and (b) all prerequisite discriminations among test samples and comparisons. After pigeons had learned two arbitrary-matching tasks (A-B and C-D), they were given a reinforced symmetry test for half of the baseline relations (B1-A1 and D1-C1). To control for the effects of reinforcement during testing, two novel, nonsymmetrical responses were concurrently reinforced using the other baseline stimuli (D2-A2 and B2-C2). Pigeons matched at chance on both types of relations, thus indicating no evidence for symmetry. These symmetrical and nonsymmetrical relations were then directly trained in order to provide exemplars of symmetry and all prerequisite discriminations for a second test. The symmetrical test relations were now B2-A2 and D2-C2 and the nonsymmetrical relations were D1-A1 and B1-C1. On this test, 1 pigeon showed clear evidence of symmetry, 2 pigeons showed weak evidence, and 1 pigeon showed no evidence. The previous training of all prerequisite discriminations among stimuli, and the within-subject control for testing with reinforcement seem to have set favorable conditions for the emergence of symmetry in nonhumans. However, the variability across subjects shows that methodological variables still remain to be controlled.     

Stimulus control topographies and tests of symmetry in pigeons

Pigeons were tested for symmetry after A-B training under conditions designed to avoid problems that may prevent its emergence, namely the change of stimulus location in testing relative to training and the lack of requisite discrimination training. In Experiment 1, samples appeared in two locations during baseline training to minimize the impact of stimulus location. Experiments 2 and 3 included multiple-location training along with additional identity and symbolic matching training, respectively, to explicitly train all of the simultaneous and successive stimulus discriminations required for testing. Experiment 4 provided reinforcement for symmetrical matching relations with some stimulus sets (with multiple-location training) prior to symmetry testing with different sets. In all experiments, pigeons showed no evidence of symmetry despite the fact that baseline (A-B) matching transferred to novel locations. Additional tests for reflexivity (Experiment 2) yielded similar outcomes. These results indicate that the change in stimulus location is not the sole reason that pigeons do not show symmetry and increase the plausibility of arguments that symmetry and other indexes of stimulus equivalence may be beyond the capabilities of the pigeon.     

Melioration, matching, and maximization

Pigeons were studied in an experiment involving two concurrently available response keys. Conditions were such that in the first condition the predictions of melioration (Herrnstein & Vaughan, 1980), minimization of deviation from matching, and maximization were identical: relative time on the right key should have fallen between .125 and .25, which in fact occurred. In the second condition, melioration predicted a shift in relative time on the right to between .75 and .875, which would involve a transient deviation from matching as well as a substantial drop in rate of reinforcement. All three birds eventually shifted their distribution of behavior to within the range predicted by melioration.     

Temporal factors influencing the pigeon's successive matching-to-sample performance: sample duration, intertrial interval, and retention interval

A successive matching-to-sample procedure that entails the sequential presentation of sample and test stimuli and the monitoring of response rates in a go/no-go discrimination of matching and nonmatching stimuli was studied as an alternative to the familiar delayed-matching paradigm of animal short-term memory. Three within-subject experiments studied the effects of sample duration (1 to 12 seconds), intertrial interval (5 to 50 seconds), and retention interval (1 to 50 seconds) on the pigeon's successive-matching performance. The results revealed that retention was (a) an increasing function of sample duration and intertrial interval, and (b) a decreasing function of retention interval. These results were in accord with those of more traditional short-term memory paradigms, and reveal the suitability of the successive-matching procedure for studying memory processes.     

A test of symmetry and transitivity in the conditional discrimination performances of pigeons

In a matching-to-sample context, pigeons were taught two conditional discriminations according to one of three equivalence paradigms: train if A, then select B and if B, then select C; train if B, then A and if B, then C; or train if A, then B and if C, then B. Test trials without reinforcement revealed that the conditional relations did not satisfy the symmetrical and transitive properties of an equivalence relation. Apparently, only specific if... then relations were learned. Contrary to Kendall's (1983) findings, and probably as a consequence of procedural differences, none of the pigeons in the present experiment were observed to emit mediating behavior during the transitivity probe trials. The absence of symmetry and transitivity may be related to the individual stimuli not being reflexive. Behavioral techniques other than the commonly used matching-to-sample technique might better succeed in avoiding unintended stimulus control in the study of the formation of stimulus classes.     

Symmetry and stimulus class formation in humans: Control by temporal location in a successive matching task

Symmetry refers to the observation that subjects will derive B‐A (e.g., in the presence of B, select A) after being trained on A‐B (e.g., in the presence of A, select B). Whereas symmetry is readily shown in humans, it has been difficult to demonstrate in nonhuman animals. This difficulty, at least in pigeons, may result from responding to specific stimulus properties that change when sample and comparison stimuli switch roles between training and testing. In three experiments with humans, we investigated to what extent human responding is influenced by the temporal location of stimuli using a successive matching‐to‐sample procedure. Our results indicate that temporal location does not spontaneously control responding in humans, although it does in pigeons. Therefore, the number of functional stimuli that humans respond to in this procedure may be half of the number of functional stimuli that the pigeons respond to. In a fourth experiment, we tested this assumption by doubling the number of functional stimuli controlling responding in human participants in an attempt to make the test more comparable to symmetry tests with pigeons. Here, we found that humans responded according to indirect class formation in the same manner as pigeons do. In sum, our results indicate that functional symmetry is readily observed in humans, even in cases where the temporal features of the stimuli prevent functional symmetry in pigeons. We argue that this difference in behavior between the two species does not necessarily reflect a difference in capacity to show functional symmetry between both species, but could also reflect a difference in the functional stimuli each species responds to.     

Concurrent-schedule performance in transition: changeover delays and signaled reinforcer ratios

Six pigeons were trained in experimental sessions that arranged six or seven components with various concurrent-schedule reinforcer ratios associated with each. The order of the components was determined randomly without replacement. Components lasted until the pigeons had received 10 reinforcers, and were separated by 10-s blackout periods. The component reinforcer ratios arranged in most conditions were 27:1, 9:1, 3:1, 1:1, 1:3, 1:9 and 1:27; in others, there were only six components, three of 27:1 and three of 1:27. In some conditions, each reinforcement ratio was signaled by a different red-yellow flash frequency, with the frequency perfectly correlated with the reinforcer ratio. Additionally, a changeover delay was arranged in some conditions, and no changeover delay in others. When component reinforcer ratios were signaled, sensitivity to reinforcement values increased from around 0.40 before the first reinforcer in a component to around 0.80 before the 10th reinforcer. When reinforcer ratios were not signaled, sensitivities typically increased from zero to around 0.40. Sensitivity to reinforcement was around 0.20 lower in no-changeover-delay conditions than in changeover-delay conditions, but increased in the former after exposure to changeover delays. Local analyses showed that preference was extreme towards the reinforced alternative for the first 25 s after reinforcement in changeover-delay conditions regardless of whether components were signaled or not. In no-changeover-delay conditions, preference following reinforcers was either absent, or, following exposure to changeover delays, small. Reinforcers have both local and long-term effects on preference. The former, but not the latter, is strongly affected by the presence of a changeover delay. Stimulus control may be more closely associated with longer-term, more molar, reinforcer effects.     

Formation of transitivity in conditional matching to sample by pigeons

Four homing pigeons were trained over 5 months in a zero-delay, “arbitrary” matching-to-sample procedure with sample and comparison stimuli presented on any of three response keys. Birds were also required to complete a fixed-ratio 10 requirement on both sample and comparison stimuli to terminate their presentation. The procedure resulted in the establishment of relations that were not specifically trained and that can be characterized by the property of transitivity in a stimulus equivalence context. This result was in contrast with the findings obtained from most previous research with nonhuman subjects.     

Effect of delay-interval stimuli on delayed symbolic matching to sample in the pigeon

In Experiment 1, food-deprived pigeons received delayed symbolic matching to sample training in a darkened Skinner box. Trials began with the illumination of the grain feeder lamp (no food sample), or illumination of this lamp, accompanied by the raising of the feeder tray (food sample). After a delay of a few seconds, the two side response keys were illuminated, one with red and one with green light, with positions counterbalanced over trials. Pecking the red (green) comparison produced grain reinforcement if the trial had started with food (no food); pecking red after a no-food sample or green after a food sample was not reinforced. Once matching performance was stable, four stimuli were presented during the delay interval, and their effects on matching accuracy were evaluated. Both illumination of the houselight and the center key with white geometric forms decreased matching accuracy, whereas presentation of a tone and vibration of the test chamber did not. In Experiment 2, pecking the red center key was reinforced with food according to a variable interval schedule. The effects of occasional brief presentations of the four stimuli used in the first experiment on ongoing pecking were assessed. The houselight and form disturbed key pecking, but the tone and vibration did not. Thus, stimuli that interfered with delayed matching also interfered with simple operant behavior. Implications of these results for theories of remembering are discussed.