Select and reject conditional control on matching to sample and stimulus equivalence

Abstract

The purpose of this study was to test Carrigan and Sidman's (1992) hypothesis that the emergence of equivalence relations from the standard matching‐to‐sample (MTS) procedure is due to the exclusive acquisition of select conditional relations during training. Four groups were compared on tests of the properties of equivalence relations (reflexivity, symmetry, and transitivity/equivalence) and on trials with novel stimuli replacing S+ or S− on these tests: standard MTS training; exclusive‐select‐relations training; exclusive‐reject‐relations training; and detached‐MTS training, which included training on both select and reject relations. Equivalence emergence occurred more frequently in the detached‐MTS group. Those in the standard‐MTS group who showed equivalence emergence had test results with novel stimuli that were more similar to those in the detached‐MTS group than to those in the exclusive‐select group. The results suggest that compliance with the criteria for equivalence relations may mask at least two different processes. The first is pseudoequivalence, which is associated with exclusive select control. The second is the authentic formation of equivalence classes, which depends on joint select and reject control. The standard‐MTS procedure seems to more frequently promote the second process.

For over 4 decades, the stimulus equivalence paradigm has been central to behavior analysis in studying symbolic behavior. Formalized by Sidman and Tailby (1982), this paradigm demonstrates the emergence of new conditional discriminations that exhibit equivalence properties—reflexivity, symmetry, and transitivity—after training arbitrary conditional discriminations. For example, given stimulus sets A, B, and C, training AB and BC (where the first letter denotes the sample stimulus and the second letter denotes the comparison stimulus) discriminations can lead to the emergence of reflexivity (AA, BB, CC), symmetry (BA, CB), and transitivity (AC, CA) relations (Green & Saunders, 1998; Sidman & Tailby, 1982).

The standard matching‐to‐sample (MTS) procedure is the most widely used method for training and assessing equivalence relations (Carter & Werner, 1978; Cumming & Berryman, 1961). This procedure involves presenting a sample stimulus followed by multiple comparison stimuli and requiring the subject to choose a comparison based on the sample. Participants can learn two types of conditional relations between each sample stimulus and the comparison stimuli: (a) selection or sample‐S+ relations with those comparison stimuli whose choice is reinforced and (b) rejection or sample‐S− relations with those comparison stimuli whose choice is not reinforced. In AB relation training with a two‐choice MTS, correct responses are obtained by choosing B1 and not B2 when faced with sample A1 and by choosing B2 and not B1 when faced with sample A2. Correct responses could be controlled by conditional select relations, reject relations, or both (Carrigan & Sidman, 1992; Sidman, 1987).

One of the primary issues in the study of stimulus equivalence relations is identifying the antecedent stimulus control conditions under which they emerge. Murray Sidman (Carrigan & Sidman, 1992; Johnson & Sidman, 1993) proposed that the emergence of equivalence relations depends exclusively on conditional select relations established during training. He argued that failures to establish equivalence relations result from the effects of reject control acquired during training. Both select and reject control mechanisms can produce equivalence relations, but these relations are mutually exclusive. For example, in training conditional relations AB and BC, select control would establish equivalence relations among stimuli A1B1C1 and A2B2C2, whereas reject control would establish equivalence relations among stimuli A1B2C1 and A2B1C2. These distinct control types yield different outcomes on reflexivity and transitivity tests but not on symmetry tests. For example, on a reflexivity trial, when presented with sample stimulus A1, select control would lead to choosing comparison stimulus A1 over A2, whereas reject control would result in choosing A2 because A1 is rejected. Some empirical evidence supports this analysis (Johnson & Sidman, 1993; Perez et al., 2015).

If select and reject control generate incompatible equivalence relations, a critical question arises concerning how stimulus equivalence can emerge using the standard MTS procedure. This procedure has the potential to simultaneously establish both conditional select and reject control. For example, Stromer and Osborne (1982) demonstrated that the two‐choice standard MTS procedure generates both conditional select and reject control using tests with novel stimuli (see also McIlvane et al., 1987, Experiment 1, for an example with the blank‐comparison procedure). Sidman (1987; Carrigan & Sidman, 1992) suggested that to minimize the influence of reject control in favor of select control, a MTS procedure with three or more comparison stimuli per trial should be employed. Given that this approach increases the number of sample‐S− relations to be learned, acquiring select control is more likely because it involves learning fewer relations (see Boelens, 2002, for a critique of this argument). However, the probability of forming equivalence relations with the two‐choice standard‐MTS procedure is high (e.g., Stromer & Osborne, 1982; Tomonaga, 1993, Experiment 2 with a chimpanzee) and not lower than with MTS with three or more comparisons (Saunders et al., 2005). Furthermore, individuals who demonstrate equivalence with the standard MTS procedure often exhibit strong performance on conditional select and reject control tests (Arantes & de Rose, 2015; Carr et al., 2000; de Rose et al., 2013; Grisante et al., 2014; Harrison & Green, 1990; Kato et al., 2008; Plazas, 2019, 2024; Plazas & Peña, 2016; Plazas & Villamil, 2016, 2018). Indeed, reject control may facilitate the expansion of equivalence class members (Plazas, 2019). Currently, the behavioral mechanisms underlying the emergence of equivalence relations with the standard MTS procedure remain unclear, particularly for the two‐choice format. This is especially significant given that much of what is known about stimulus equivalence has been derived from studies using the standard MTS procedure.

One limitation of previous research is that traditional tests of stimulus equivalence properties do not allow determination of whether the stimulus control underlying the emergence of equivalence in the standard MTS procedure is based on select control or a combination of select and reject control. To address this issue, the current study adopted Stromer and Osborne's (1982) strategy of introducing novel stimuli (N) to replace either the S− or S+ on trials testing the properties of equivalence. This study compared the performance on equivalence tests by participants who were trained with the standard two‐choice MTS procedure with that of participants who were trained under three different conditions: (1) conditional relations that promoted select control, (2) conditional relations that promoted reject control, and (3) conditional relations that promoted both select and reject control (termed the detached‐MTS group). An analysis based on Carrigan and Sidman (1992) predicts clear differences in the responses by each group to test trials with novel stimuli as follows.

Suppose that participants are trained on AB and BC conditional relations that promote either select or reject control, and then tested for reflexivity, symmetry, and transitivity with trials in which a novel stimulus (N) replaces either S− or S+. According to Carrigan and Sidman's (1992) analysis, training to promote select control should result in participants learning “A1 select B1,” “A2 select B2,” “B1 select C1,” and “B2 select C2,” whereas training to promote reject control should result in participants learning “A1 reject B2,” “A2 reject B1,” “B1 reject C2,” and “B2 reject C1.” On transitivity trials where S− is replaced by a novel stimulus N, the two types of training should produce different responses. For example, with A1 as the sample and C1 and N as the comparisons, those trained on select control should respond to C1, whereas those trained on reject control should respond to N (because C1 controls a reject response to A1). However, both groups should have no basis for responding on trials where N replaces S+ (e.g., A1 as sample and N and C2 as comparisons) and may show inconsistent performance. In contrast, the detached‐MTS group, trained on both select and reject control, should respond inconsistently on trials where N replaces the S− and on trials where N replaces the S+. These predictions are illustrated in Table 1. The same should be true for reflexivity trials with novel stimuli for each of these three types of training. For symmetry trials with N stimuli, the predictions are different. When N replaces the S− (e.g., B1 sample and A1 and N comparisons), those trained on select relations should respond to A1, whereas those trained on reject relations should respond inconsistently. In contrast, when N replaces the S+ (e.g., B1 sample and N and A2 comparisons), participants in the select group should respond inconsistently and those in the reject group should respond to N. Participants in the detached‐MTS group should have a double basis for responding, choosing A1 when N replaces the S− and N when it replaces the S+. Differences in reaction times would also be expected to be greater and responses expected to be inconsistent on test trials where the baseline did not allow to determining the correct response (see Table 1). If equivalence relations in the standard MTS procedure arise only from conditional select relations, then the performance of participants trained with this procedure on trials with novel stimuli should be similar to that of participants trained to promote select relations.

TABLE 1.

Predicted responses on test trials with novel stimuli for each type of training.

	Reflexivity			Symmetry			Transitivity/Equivalence
	N−	N+		N−	N+		N−	N+
Exclusive conditional select control	Baseline stimulus	Inconsistent		Baseline stimulus	Inconsistent		Baseline stimulus	Inconsistent
Exclusive conditional reject control	N stimulus	Inconsistent		Inconsistent	Baseline stimulus		N stimulus	Inconsistent
Conditional select and reject control (Detached‐MTS)	Inconsistent	Inconsistent		Baseline stimulus	Baseline stimulus		Inconsistent	Inconsistent

Note: N− and N+ correspond to test trials where S‐ and S+ are replaced by a novel stimulus, respectively. According to Carrigan and Sidman's (1992) analysis, the three training conditions indicated would have three types of possible responses to the test trials—namely, responding to one of the stimuli trained in the baseline, responding to the novel stimulus, or presenting inconsistent responses.

METHOD

Participants

Forty‐eight first‐year psychology students from a private university participated, recruited through convenience sampling. The sample consisted of 35 females and 13 males, with ages ranging from 17 to 28 years (M = 19.4, SD = 3.7). No other demographic information was collected. A block randomization procedure was used to assign each participant to one of four groups, each consisting of 12 individuals. All participants provided informed consent prior to the experiment and received financial compensation equivalent to approximately US$7.21 (in local currency) for completing all phases. Participants who withdrew early received one third of this amount.

Apparatus and stimuli

The experimental task was performed on a computer, with participants seated individually at workstations equipped with headphones for auditory feedback. The workstations were separated by partitions to prevent visual contact between participants. The stimuli included letters from various non‐Latin alphabets, presented in black on a white background and sized 3.5 × 3.5 cm (see Figure 1). Each stimulus was assigned an alphanumeric code for identification. Training stimuli consisted of six items labeled A, B, and C (A1, A2, B1, B2, C1, C2), designed to form two equivalence classes of three members each. Additional stimuli (16 labeled W, X, Y, and Z) were used to bias responses toward either exclusive select or exclusive reject relations, based on the procedure established by Carrigan and Sidman (1992) and implemented in subsequent research (e.g., Johnson & Sidman, 1993; Perez et al., 2015, 2019. 2020; Plazas, 2024). Eight N stimuli were used on test trials. The experimental task was programmed using Psytoolkit (Stoet, 2010, 2017) to administer trials and record responses.

FIGURE 1.

Stimuli used in the study.

Procedure

Before beginning the training phases, participants completed a brief demographic survey and then received the following instructions in Spanish:

Figures will appear on the screen hidden behind a black square. Click the “LOOK” button below the black square to see the hidden figure. Each trial begins with the presentation of a hidden figure (behind a black square) in the center of the screen. After you view this figure, two more hidden figures will appear in the bottom corners. Once you have looked at each of them, you must choose one of them. To choose a particular figure, click on the “CHOOSE” button below the figure. Correct choices will be followed by a dot added to a counter and a ta‐da tone; incorrect choices will be followed by a dissonant sound. One more important thing: Sometimes you are not allowed to see one of the corner figures. Even if you cannot see it, you must continue. Your goal is to make as many correct choices as possible. Always try to score— have fun playing!

The MTS with observation requirement (MTS−OR) procedure, developed by Perez et al. (2015, 2020), was employed. In this procedure, stimuli initially appear masked by a black square, requiring participants to make an observing response (OR) to unmask the stimulus. Below each stimulus was a button labeled “MIRAR” (“LOOK” in English), which participants used to make the OR. Upon clicking the OR button, the black square disappeared, revealing the stimulus for 0.3 s before the black square reappeared. Each trial began with the presentation of a masked sample stimulus at the top center of the screen, accompanied by an OR button below it. When the participant made an OR, the sample stimulus was displayed and the comparison stimuli—also masked by black squares—appeared at the bottom of the screen, each with its own OR button. Clicking an OR button for a comparison stimulus revealed it for 0.3 s, after which the black square reappeared. Once both comparison stimuli were observed, the word “LOOK” on the buttons changed to white, rendering the OR buttons inactive. Subsequently, two additional buttons labeled “ELEGIR” (“CHOOSE” in English) appeared below the comparison stimuli, allowing the participant to select one of the comparisons. Correct choices triggered a “ta‐da” sound and awarded a point displayed on a counter at the top of the screen, whereas incorrect choices produced a dissonant “chord” sound. Following feedback, a 0.5‐s intertrial interval was presented during which only the counter remained visible. Depending on the experimental group, during training and baseline trials for the exclusive‐select, exclusive‐reject, and detached groups, half of the ORs to either the S+ or S− did not display the corresponding comparison stimulus, as described in detail later.

Training phases

The distinction among the four groups involved the implementation of two procedures: (1) Sidman and colleagues' method for biasing control toward exclusive‐select or exclusive‐reject relations, and (2) Perez and colleagues' method for biasing attention toward the S+ or S− stimuli during training trials. Sidman's procedure (Carrigan & Sidman, 1992; Johnson & Sidman, 1993) biases control toward exclusive‐select relations by requiring participants to learn more sample‐S− than sample‐S+ relations, using W and Z stimuli in training. Conversely, control is biased toward exclusive‐reject relations by requiring participants to learn more sample‐S+ than sample‐S− relations, using X and Y stimuli. The rationale is that participants are more likely to learn the less frequently presented relation. Perez's procedure (Perez et al., 2015, 2019, 2020) biases attention by manipulating the unmasking of stimuli. For attention to the S+, the unmasking of the S− is prevented on 50% of the instances participants make the OR for that stimulus. Similarly, attention is biased toward the S− by preventing the unmasking of the S+ under equivalent conditions. The four groups differed in their application of these procedures. The standard‐MTS group received no control or attention‐biasing procedures but underwent training with the MTS−OR protocol. The exclusive‐select group received both the control‐ and attention‐biasing procedures toward the S+. The exclusive‐reject group received these procedures directed toward the S−. Last, the detached‐MTS group received the control‐ and attention‐biasing procedures targeting both S+ and S− in alternating trials. Participants in the first three groups underwent four training phases, and those in the detached‐MTS group underwent eight phases due to the alternation of procedures. Table 2 outlines the trial types presented during the training phases across the groups. Detailed descriptions of each groups training are provided below.

TABLE 2.

Trial types in training phases.

	Standard‐ MTS			Exclusive‐Select			Exclusive‐Reject			Detached‐MTS
Phase	Ss	S+	S−	Ss	S+	S−	Ss	S+	S−	Phase	Ss	S+	S−
1	A1	B1	B2	A1	B1	B2	A1	B1	B2	1	A1	B1	B2
	A2	B2	B1	A1	B1	W1	A1	X1	B2		A1	B1	W1
				A1	B1	W3	A1	X3	B2		A1	B1	W3
				A2	B2	B1	A2	B2	B1		A2	B2	B1
				A2	B2	W2	A2	X2	B1		A2	B2	W2
				A2	B2	W4	A2	X4	B1		A2	B2	W4
										2	A1	B1	B2
											A1	X1	B2
											A1	X3	B2
											A2	B2	B1
											A2	X2	B1
											A2	X4	B1
										3	Trials of Phases 1 and 2
2	B1	C1	C2	B1	C1	C2	B1	C1	C2	4	B1	C1	C2
	B2	C2	C1	B1	C1	Z1	B1	Y1	C2		B1	C1	Z1
				B1	C1	Z3	B1	Y3	C2		B1	C1	Z3
				B2	C2	C1	B2	C2	C1		B2	C2	C1
				B2	C2	Z2	B2	Y2	C1		B2	C2	Z2
				B2	C2	Z4	B2	Y4	C1		B2	C2	Z4
										5	B1	C1	C2
											B1	Y1	C2
											B1	Y3	C2
											B2	C2	C1
											B2	Y2	C1
											B2	Y4	C1
										6	Trials of Phases 4 and 5
3	AB and BC trials									7	AB and BC trials
4	Learning test									8	Learning test

Note: “Ss,” “S+,” and “S−” correspond to sample stimulus, S+ comparison stimulus, and S− comparison stimulus, respectively.

Standard‐MTS group

This group underwent four phases of training. In the first phase, participants were trained on AB relations by presenting sample stimuli (A1 and A2) sequentially, with comparison stimuli (B1 and B2) presented simultaneously. B1 was the correct choice after A1, and B2 was the correct choice after A2. In the second phase, participants were trained on BC relations, where B1 and B2 were presented as sample stimuli, with C1 being correct after B1 and C2 being correct after B2. The left–right positioning of the S+ and S− stimuli was counterbalanced across trials. These phases were presented in blocks of 24 trials, with a mastery criterion of 23/24 correct responses. On all trials, the ORs always unmasked the comparison stimuli. In the third phase, trials of AB and BC relations were intermixed in blocks of 24 trials and there was a mastery criterion of 22/24 correct responses. The final phase was a feedback‐free learning test using the same trials as in Phase 3, and participants had to meet the same criterion in a single block of 24 trials to proceed. Participants were informed in advance that no feedback would be provided in this phase. Those who met the criterion proceeded to the test phases, but those who failed to meet the criterion were returned to Phase 3.

Exclusive‐select group

This group trained under conditions to promote select control and bias attending toward the S+. Phase 1 included trials with A1 as the sample; B1 as the S+; and B2, W1, or W3 as the S− and trials with A2 as the sample; B2 as the S+; and B1, W2, or W4 as the S−. Phase 2 presented trials with B1 as the sample; C1 as the S+; and C2, Z1, or Z3 as the S− and trials with B2 as the sample; C2 as the S+; and C1, Z2, or Z4 as the S− (see Table 2). Across both phases, S+ stimuli were always unmasked during ORs but S− stimuli were unmasked only half of the time. The third phase intermixed AB and BC trial types, with feedback. In the fourth phase, participants completed a feedback‐free learning test using the same trials as in the previous phase. Participants who did not meet the mastery criterion in this phase were returned to the prior phase. The number of trials per block and mastery criterion across the phases were the same as they were for the standard‐MTS group.

Exclusive‐reject group

This group followed a protocol similar to that for the exclusive‐select group, but training promoted reject control and biasing attention toward the S−. In Phase 1, when A1 was the sample, S+ stimuli included B1, X1, or X3 and B2 was the S−. When A2 was the sample, S+ stimuli included B2, X2, or X4 and B1 as the S−. In Phase 2, when B1 was the sample, S+ stimuli included C1, Y1, or Y3 and C2 was the S−. Similarly, when B2 was the sample, S+ included C2, Y2, or Y4 and C1 was the S− (see Table 2). Across these phases, S+ stimuli were consistently unmasked and S− stimuli were unmasked only half of the time. Phase 3 intermixed the trial types from the previous two phases, followed by a feedback‐free learning test in Phase 4. The number of trials per block and mastery criterion for each phase were the same as those for the standard‐MTS and exclusive‐select groups.

Detached‐MTS group

This group required eight phases of training due to the alternation of control‐ and attention‐biasing procedures toward both the S+ and S−. Phases 1 and 2 trained AB relations, with Phase 1 emphasizing biasing toward S+ (similar to the exclusive‐select group) and Phase 2 emphasizing biasing toward S− (similar to the exclusive‐reject group). The blocks in these phases had 24 trials, with a criterion of 23/24 correct responses. In Phase 3, AB relations from the first two phases were intermixed in blocks of 24 trials and the criterion was 22/24 correct. Phases 4 and 5 trained BC relations, with Phase 4 emphasizing biasing toward the S+ and Phase 5 emphasizing biasing toward the S−. Phase 6 intermixed BC relations from Phases 4 and 5. Phases 4–6 shared the same number of trials per block and mastery criterion as the first three phases. In Phase 7, all AB and BC relations from the previous phases were intermixed, in blocks of 48 trials, with a criterion of 44/48 correct. All trials up to this point had feedback. The final phase, Phase 8, was a feedback‐free learning test using the same trials and mastery criterion as Phase 7. Those who failed in the learning‐test phase were returned to the preceding phase for additional practice.

Testing phases

Participants in all four groups completed the same testing phases, presented in the same order. First, a conditional control test was administered, followed by the AC transitivity test, the BA and CB symmetry tests, the CA combined transitivity/symmetry (equivalence) test, and finally the AA, BB, and CC reflexivity tests. This sequence mirrors the methodology of Perez et al. (2015, 2019, 2020). For the standard‐MTS, exclusive‐select, and exclusive‐reject groups, these tests corresponded to Phases 5 through 12, and for the detached‐MTS group, they corresponded to Phases 9 through 16.

In all phases, baseline trials were intermixed with test trials to assess the maintenance of baseline responses. For the standard‐MTS, exclusive‐select, and exclusive‐reject groups, 12 baseline trials were included per phase, with each trial type presented three times for the standard‐MTS group and once for the exclusive‐select and exclusive‐reject groups. For the detached‐MTS group, there were 16 baseline trials, eight select control trials (four AB and four BC), and eight reject control trials (four AB and four BC) in each phase. The set of baseline trial types varied between phases for this group. Across all groups, baseline trials maintained the control‐ and attention‐biasing conditions established during training, although no feedback was provided for these trials.

Table 3 presents the test trials for each phase. After completing the learning test phase, participants underwent a conditional control test phase. In addition to baseline trials, this phase included trials assessing AB and BC conditional relations, with novel stimuli replacing either the S− or S+ comparison stimuli. Specifically, there were eight trials in which a novel stimulus (N) replaced the S− comparison stimulus to evaluate select conditional control without using the baseline W and Z stimuli. Similarly, eight trials featured an N stimulus replacing the S+ comparison stimulus to assess reject conditional control without involving baseline X and Y stimuli.

TABLE 3.

Trial types in test phases.

	Standard‐MTS, Exclusive‐select, Exclusive‐reject phase	Detached‐MTS phase	Test trials			N− test trials				N+ test trials
Test			Ss	S+	S−	Ss	S+	S−		Ss	S+	S−
Conditional Control	5	9				A1	B1	N		A1	N	B2
						A2	B2	N		A2	N	B1
						B1	C1	N		B1	N	C2
						B2	C2	N		B2	N	C1
Transitivity AC	6	10	A1	C1	C2	A1	C1	N		A1	N	C2
			A2	C2	C1	A2	C2	N		A2	N	C1
Symmetry BA	7	11	B1	A1	A2	B1	A1	N		B1	N	A2
			B2	A2	A1	B2	A2	N		B2	N	A1
Symmetry CB	8	12	C1	B1	B2	C1	B1	N		C1	N	B2
			C2	B2	B1	C2	B2	N		C2	N	B1
Equivalence CA	9	13	C1	A1	A2	C1	A1	N		C1	N	A2
			C2	A2	A1	C2	A2	N		C2	N	A1
Reflexivity AA	10	14	A1	A1	A2	A1	A1	N		A1	N	A2
			A2	A2	A1	A2	A2	N		A2	N	A1
Reflexivity BB	11	15	B1	B1	B2	B1	B1	N		B1	N	B2
			B2	B2	B1	B2	B2	N		B2	N	B1
Reflexivity CC	12	16	C1	C1	C2	C1	C1	N		C1	N	C2
			C2	C2	C1	C2	C2	N		C2	N	C1

Note: “Ss,” “S+,” and “S−” as in Table 2. “N−” means trials in which a novel stimulus replaced the S− comparison stimulus on a test trial. “N+” means trials in which a novel stimulus replaced the S+ comparison stimulus on a test trial. “N” is a novel stimulus. The N stimuli were randomly selected from a set of eight stimuli for each of the trials in which they appeared (see Figure 1).

Following the conditional control phase, participants completed the AC transitivity test phase. This phase included eight AC test trials, eight AC transitivity trials in which an N stimulus replaced the S−, and eight AC trials in which an N stimulus replaced the S+ (henceforth, N− and N+ trials, respectively). All trial types were randomized and presented intermixed with baseline trials. Subsequent symmetry, equivalence, and reflexivity test phases followed the same structure, each consisting of four types of trials: baseline trials, eight test‐specific trials, eight N− trials, and eight N+ trials (see Table 2). The total number of trials per phase was 36 for the standard‐MTS, exclusive‐select, and exclusive‐reject groups and 40 for the detached‐MTS group.

If participants exhibited baseline deterioration in any test phase, they were retrained on the AB and BC relations, with blocks of Phase 3 (Phase 7 for the detached‐MTS group) and reassessed with the learning test. Then, they repeated the corresponding test phase. The retraining criterion was nine or fewer correct baseline responses in the standard‐MTS, exclusive‐select, and exclusive‐reject groups or 13 or fewer correct responses for the detached‐MTS group. Participants who failed to meet the baseline maintenance criterion after three retraining attempts in a single test phase were removed from the experiment.

Conversely, participants who did not meet specific criteria on exclusive test trials (i.e., transitivity, symmetry, equivalence, or reflexivity test trials, without N stimuli) were reexposed to the same phase once after completing all test phases. The reexposure criterion for the standard‐MTS, exclusive‐select, and detached‐MTS groups was six or fewer correct responses. For the exclusive‐reject group, the criterion was six or fewer correct responses on symmetry trials and three or more correct responses on transitivity, equivalence, or reflexivity trials.

RESULTS

Table 4 presents the number of blocks required by participants in each group to meet the established criteria during the training phases. Participants in the standard‐MTS group required between 1 and 7 blocks (M = 2.8) to complete Phase 1, between 1 and 3 blocks (M = 1.5) to complete Phase 2, and 1 and 6 blocks (M = 1.8) to complete Phase 3. All completed the learning test in 1 block except P5, who required two exposures (M = 1.1). Participants in the exclusive‐select group needed between 2 and 11 blocks (M = 4.2) for Phase 1, between 1 and 5 blocks (M = 2.1) for Phase 2, and 1 and 9 blocks (M = 2.2) for Phase 3. All completed the learning test in a single exposure except P23 and P24, who required five and two exposures, respectively (M = 1.4). In the exclusive‐reject group, participants required between 2 and 8 blocks (M = 3.7) for Phase 1, between 1 and 16 blocks (M = 4.8) for Phase 2, and 1 and 10 blocks (M = 3.6) for Phase 3. Most participants completed the learning test in one exposure; however, P30 and P33 required four exposures (M = 1.8). For the detached‐MTS group, participants (excluding P48) required from 1 to 4 blocks (M = 2.4) for Phase 1, 1 to 2 blocks (M = 1.9) for Phase 2, and 1 to 12 blocks (M = 4.9) for Phase 3. Phase 4 was completed in 1 to 3 blocks (M = 1.6), Phase 5 in 1 to 6 blocks (M = 1.8), Phase 6 in 1 to 2 blocks (M = 1.3), and Phase 7 in 1 to 5 blocks (M = 1.6). All participants completed the learning test in a single exposure. P48 required between 8 and 20 blocks for Phases 1 to 5 but withdrew from the experiment during Block 11 of Phase 6.

TABLE 4.

Number of blocks in training phases.

		Phase
Group	Part			1			2	3	4
Standard‐MTS	1			3			2	1	1
	2			2			3	1	1
	3			1			1	1	1
	4			2			1	2	1
	5			2			1	3	2
	6			3			1	1	1
	7			7			2	1	1
	8			2			1	2	1
	9			2			1	1	1
	10			4			1	1	1
	11			3			2	6	1
	12			2			2	1	1
Exclusive‐select	13			11			2	1	1
	14			2			3	1	1
	15			6			2	3	1
	16			3			2	1	1
	17			4			2	1	1
	18			2			2	1	1
	19			3			1	1	1
	20			2			1	1	1
	21			4			1	1	1
	22			5			1	1	1
	23			3			3	9	5
	24			5			5	5	2
Exclusive‐reject	25			2			3	1	1
	26			3			2	1	1
	27			8			3	2	2
	28			3			1	1	1
	29			4			1	2	1
	30			7			3	10	4
	31			2			16	7	2
	32			2			3	3	1
	33			6			10	10	4
	34			2			3	2	1
	35			2			10	3	3
	36			3			2	1	1

	Phase
		1	2	3	4	5	6	7	8
Detached‐MTS	37	2	2	10	2	6	1	2	1
	38	3	2	2	1	1	1	1	1
	39	2	2	5	2	1	1	1	1
	40	2	2	2	2	2	1	3	1
	41	2	2	4	2	1	1	1	1
	42	1	2	1	1	1	2	1	1
	43	2	2	12	3	2	1	1	1
	44	4	2	1	2	1	1	1	1
	45	2	1	1	1	1	1	1	1
	46	3	2	12	1	2	1	1	1
	47	3	2	4	1	2	3	5	1
	48	20	8	20	20	9	11	0	0

Note: “Part” stands for participant number. The phases of the first three groups were aligned with those of the detached MTS group according to their content.

Two distinct criteria were used to assess the formation of equivalence relations: one for “select equivalence” relations and another for “reject equivalence” relations. The criterion for select equivalence relation formation was at least 87.5% correct responses on test trials assessing transitivity, symmetry, equivalence, and reflexivity. In contrast, the criterion for reject equivalence relation formation was no more than 12.5% correct on transitivity, equivalence, and reflexivity tests and at least 87.5% correct responses on symmetry tests. These criteria align with those established by Carrigan and Sidman (1992). Performance on the N− and N+ tests was categorized as “high” if it was over 87.5% correct and as a “reversal of expected relations” if it was below 12.5% correct. Reversals were considered accurate because they demonstrated consistent response patterns and provided valuable insights, as discussed below.

Figures 2, 3, 4, 5 through 2, 3, 4, 5 present the proportion of correct responses for each type of test trial during the test phases for each participant across all groups. White bars represent baseline trials, black bars represent equivalence test trials (i.e., transitivity, symmetry, equivalence, and reflexivity), light gray bars represent N− test trials, and dark gray bars represent N+ test trials. In the conditional control phase, only the baseline, N−, and N+ test bars are presented. Participants could undergo a test phase multiple times, after either retraining (if baseline criteria were not met) or retesting (if test criteria were not met). However, only the final test phase exposure is reported (i.e., after retraining or retesting if applicable). Only data from the reported phase were analyzed. The following indices indicate the phase associated with each group of bars: No index corresponds to the initial presentation of the test phase, “a” denotes the first retraining phase, “b” denotes the second retraining phase, “c” denotes the retesting phase, and “d” denotes that the phase was not presented because the participant withdrew from the study.

FIGURE 2.

Results of standard‐MTS group on tests. “CO” corresponds to the tests from the conditional control phase. Bars present the proportion of correct responses on each test type. White bars are for baseline trials, black bars are for the properties of equivalence trials, light gray bars are for N− trials, and dark gray for N+ trials. Index “a” means results after the first retraining, “b” means results after the second retraining, “c” means results of the retesting, and “d” means the participant withdrew.

FIGURE 3.

Results of exclusive‐select group on tests.

FIGURE 4.

Results of exclusive‐reject group on tests.

FIGURE 5.

Results of detached‐MTS group on tests.

Figure 2 shows the results of the standard‐MTS group on the equivalence relation and novel stimulus tests. In the conditional control phase, all participants showed high performance on the baseline and select‐control trials. Half of the participants showed high performance on reject‐control trials (P1, P3, P5, P9, P10, and P12), and P4 exhibited response reversal. Half of the participants met the select equivalence criterion (P1, P2, P3, P4, P9, and P12). Of these participants, three (P1, P3, and P9) showed high performance on the N− and N+ trials and one (P12) showed high performance on all N− trials and 6/8 N+ trials. Participants P2 and P4 showed perfect performance on N− trials but low performance (P2) or reversal (P4) on N+ trials. Three participants (P7, P10, P11) met the criterion on 5/7 equivalence properties tests, had perfect (P7) or high performance on N− trials, and demonstrated irregular performance or a reversal (P7) on N− trials. Participants P5, P6, and P8 had highly inconsistent performance on all types of trials as well a baseline deterioration. P6 showed a curious pattern of reversal on all equivalence (CA) test trials and the BB and CC reflexivity tests.

Figure 3 shows the results of the exclusive‐select group in the test phases. In the conditional control phase, nine participants showed high performance on the baseline trials, with the exception of P13, P16, and P23 (although P13 and P16 had 10/12 correct responses). All participants showed high performance on the select‐control test, and 10 participants had response reversals on the reject‐control test (except for P20 and P23). P23 terminated the task after failing to meet the baseline criterion three times in the conditional control phase. The remaining participants showed high or perfect performance on N− trials (except P20), and most showed reversals on all or most N+ trials. Only two participants reached the criterion for select‐control equivalence (P19 and P22). They had perfect performance on N− trials and perfect reversals on N+ trials. Four participants (P13, P18, P20, and P21) met the criterion on 5/7 or 6/7 equivalence tests, with perfect or high performance on N− trials and perfect reversal or inconsistent results on N+ trials. The remaining participants presented irregular performance on tests for the properties of equivalence.

Figure 4 shows the results of the exclusive‐reject group on test trials. Most participants were retested. In the conditional control phase, five participants showed high performances on the baseline trials, although the remaining participants had 10/12 correct responses. On the select‐control test trials, P26 showed high performances and the remaining participants exhibited response reversals (except for P29 and P36). All participants showed high performance on the reject‐control test, except for P29. One participant (P29) met the criterion for select equivalence and had high scores on all N− and N+ tests. P31 and P36 met the select‐equivalence criterion on 6/7 tests, with irregular performance on N− tests and irregular (P31) or high performance on most N+ tests. None of the participants showed the pattern for reject‐control equivalence. P26 and P28 showed response reversals or very low scores on transitivity and equivalence trials and high scores on symmetry, but both had high scores on all reflexivity tests. Interestingly, on the reflexivity tests, they showed high responses on N− trials and inconsistent responses on N+ trials, shifting their response patterns with respect to previous phases. Other participants showed some characteristic reversals of reject equivalence: P26 on AC, P27 on BB, P33 on AC and AA, and P32 on all reflexivity tests. They predominantly showed a pattern of reversal on N− trials and high performance on N+ trials on these tests. The remaining participants did not show clear patterns or consistent performance across properties of equivalence tests, and some showed deterioration on baseline trials.

Figure 5 shows the results in the test phases for the participants in the detached‐MTS group. The results of participant P48 are not shown because he dropped out before completing the training phases. In the conditional control phase, all participants showed high performance on the baseline and select‐control trials and nine participants also on the reject‐control trials (with the exception of P43 and P47). In this group, eight participants reached the select‐equivalence criterion (P37, P38, P40, P41, P42, P44, P45, P46). Of these, six (P40, P41, P42, P44, P45, P46) showed high scores on all or most N− and N+ tests. P37 showed high scores on most N+ trials and inconsistent scores on N− trials, and P38 showed the reverse pattern. Two other participants, P39 and P47, showed high scores on 6/7 tests of the equivalence properties. P39 scored high on most N+ tests but had inconsistent results on N− tests, whereas P47 showed the opposite pattern. P43 presented inconsistent responses on all types of tests across the phases. Participants in this group required the least amount of retraining or reexposure to the tests.

Table 5 presents the percentage of N+ and N− tests by group, divided into reflexivity, symmetry, and transitivity tests in which participants consistently responded to either the baseline or the novel stimulus. These results should be compared with the predictions in Table 1. As expected, participants in the exclusive‐select group consistently selected the baseline stimulus on N− trials. However, they also consistently responded to the baseline stimulus on N+ trials, indicating a strong tendency to avoid the novel stimulus and respond to the familiar stimulus, even though it belonged to the opposite stimulus class than the sample. Participants in the exclusive‐reject group chose the novel stimulus more on the N− trials of transitivity/equivalence (AC and CA) tests, as expected, and they did so on the symmetry trials as well. However, contrary to expectations, they responded more to the baseline stimulus on the N− trials of the reflexivity tests. In the N+ trials, there was a tendency to respond consistently to the novel stimulus, although this was only expected for the symmetry tests. This seems to show control by the familiar stimulus, with a response topography based on reject‐control relations, even though the familiar stimulus was of a different “reject class” than the sample. Participants in the detached‐MTS group responded consistently to all N− and N+ tests, even though this was expected only for symmetry. On N− trials they responded to the baseline stimulus, but on the N+ trials, they responded to the novel stimulus. These performances were consistent with the formation of equivalence classes. The standard‐MTS group showed consistent responses to the baseline stimulus on the N− trials, as did the exclusive‐select and detached‐MTS groups. However, on the N+ symmetry trials, they showed greater consistent responses to the novel stimulus, as did the exclusive‐reject and detached‐MTS groups. On the N+ reflexivity and transitivity‐equivalence trials, the percentage of consistent responses to the baseline and novel stimuli were similar.

TABLE 5.

Percentage of N+ and N− tests with consistent responses for each group.

	Reflexivity				Symmetry				Transitivity/Equivalence
	N−		N+		N−		N+		N−		N+
	BL	N	BL	N	BL	N	BL	N	BL	N	BL	N
Standard‐MTS group	77.8	5.6	33.3	36.1	91.7	0	25	50	75	8.3	37.5	33.3
Exclusive‐select group	100	0	78.8	9.1	100	0	77.3	0	90.9	0	81.8	4.5
Exclusive‐reject group	47.1	32.4	5.9	67.6	25	50	8.3	70.8	12.5	54.2	4.2	62.5
Detached‐MTS group	90.9	0	0	81.8	86.4	0	0	81.8	72.7	4.5	4.5	68.2

Note: The table presents the percentage of N− and N+ tests in which participants made consistent responses, whether responding to the baseline stimulus (BL) or the novel stimulus (N). The percentage is separated for reflexivity, symmetry, and transitivity tests.

Table 6 shows the mean correct responses on the tests by group. The one‐way Kruskal–Wallis test was applied to compare the groups in each test, and the Dunn post hoc test was used to establish differences between the pairs of groups. The Kruskal–Wallis test statistics and the Dunn test's z values are presented in Table 6. On the tests of the equivalence properties, the standard‐MTS and detached‐MTS groups generally presented the highest accuracy, with no statistical differences between them, whereas the exclusive‐select and exclusive‐reject groups presented lower accuracies, with no differences between them. The exclusive‐select group performed with lower accuracy on the symmetry tests than the standard‐MTS group and with lower accuracy on the BA, CA, and AA tests than the detached‐MTS group. The exclusive‐reject group scored lower on the transitivity and reflexivity tests than the standard‐MTS group (as expected) and in all tests relative to the detached‐MTS group. On the N− tests, the standard‐MTS, detached‐MTS, and exclusive‐select groups did not differ and they had higher accuracies than the exclusive‐reject group in almost all cases. On N+ tests, the standard‐MTS, detached‐MTS, and exclusive‐reject groups did not differ in most cases, and all three differed from the exclusive‐select group in almost all tests.

TABLE 6.

Statistical analysis of number of correct responses on each test type by group.

		Mean of correct responses				Kruskal–Wallis statistic	Dunn's post hoc test z score
	Test	Standard	Select	Reject	Detached		Sta‐Sel	Sta‐Rej	Det‐Sta	Rej‐Sel	Det‐Sel	Det‐Rej
Tests for equivalence relations	AC	6.1	4.6	4.1	6.0	7.2	1.4	2.0*	0.3	−0.6	1.7	2.3*
	BA	7.6	6.0	5.7	7.3	14.2**	2.1*	3.0**	0.1	−0.9	2.2*	3.1**
	CB	7.7	5.9	5.5	6.8	13.7**	2.4*	3.4***	−1.0	−1.1	1.4	2.4*
	CA	6.4	5.3	4.5	6.9	11.8**	1.7	2.6**	0.4	−0.9	2.1*	3.0**
	AA	6.6	5.9	5.2	7.3	7.8*	1.0	1.4	1.1	−0.4	2.2*	2.5*
	BB	6.3	6.3	4.8	7.3	6.7	0.2	1.2	1.4	−1.0	1.6	2.6*
	CC	6.7	6.0	5.1	7.2	5.6	0.6	1.3	1.0	−0.8	1.5	2.3*
Tests with an N stimulus replacing S‐	CO(N−)	7.8	8.0	1.3	7.3	34.3***	−0.9	4.4***	0.1	−5.3***	−0.8	4.5***
	AC(N−)	7.0	6.8	1.9	5.4	18.2***	−0.5	3.4***	−1.3	−3.9***	−1.8	2.1*
	BA(N−)	7.5	7.3	3.0	6.9	19.1***	−0.2	3.6***	−0.5	−3.8***	−0.7	3.1**
	CB(N−)	8.0	7.3	2.7	6.9	23.7***	0.5	4.4***	−1.5	−3.9***	−1.0	2.9**
	CA(N−)	6.5	7.0	2.7	6.7	15.1**	−0.4	3.1**	−0.4	−3.5***	−0.8	2.7**
	AA(N−)	7.2	7.3	4.3	6.9	16.0**	−0.3	3.3**	−0.4	−3.6***	−0.8	2.8**
	BB(N−)	6.7	7.3	4.1	7.0	9.2*	−1.1	1.9	0.1	−3.0**	−1.0	2.0*
	CC(N−)	6.8	7.3	4.5	7.3	11.7**	−0.7	2.2*	0.7	−2.9**	0.0	2.9**
Tests with an N stimulus replacing S+	CO(N+)	5.4	0.5	7.8	6.8	29.1***	3.0**	−2.1*	1.1	5.1***	4.1***	−1.0
	AC(N+)	3.3	1.1	6.3	5.8	18.0***	1.8	−2.0*	1.6	3.8***	3.4***	−0.4
	BA(N+)	5.4	0.8	6.8	6.8	23.3***	2.8**	−1.5	1.3	4.3***	4.1***	−0.2
	CB(N+)	4.6	0.7	6.5	6.7	20.6***	2.4*	−1.5	1.5	3.9***	4.0***	0.1
	CA(N+)	4.0	1.1	5.9	6.7	20.3***	2.2*	−1.3	1.9	3.5***	4.2***	0.6
	AA(N+)	4.3	1.1	6.2	6.8	20.4***	2.4*	−1.2	1.8	3.5***	4.2***	0.6
	BB(N+)	4.1	1.2	5.8	6.7	18.3***	2.1*	−1.3	1.8	3.4***	3.9***	0.5
	CC(N+)	3.3	1.0	6.3	6.8	18.5***	1.8	−1.7	2.0*	3.5***	3.8***	0.3

Note: The Dunn post hoc test columns show the z scores for the comparisons of each pair of groups. “Sta,” “Sel,” “Rej,” and “Det” are for the standard‐MTS, exclusive‐select, exclusive‐reject, and detached‐MTS groups, respectively.

^* p < .05.

^** p < .01.

^*** p < .001.

Reaction times were also measured on the test trials. Reaction times were measured as the difference between the second OR to the comparison stimuli and the response to one of the “CHOOSE” buttons. Figure 6 shows the average of the differences in reaction times between the responses on the equivalence test trials and the responses on the N− and N+ trials across all test phases for the four groups. The differences between the responses on the equivalence test trials and the N− trials are positive for exclusive‐select (M = 129 ms) and exclusive‐reject (M = 40 ms) groups, indicating that overall responding to the N− trials was faster than to the equivalence test trials for these groups. In contrast, for the standard‐MTS (M = −4 ms) and detached‐MTS groups (M = −6 ms) the differences were minimal. The four groups presented negative differences between the response to the equivalence test trials and the N+ test trials, showing that participants generally required more time to choose on the N+ trials, although these differences were higher for the standard‐MTS (M = −143 ms) and detached‐MTS (M = −148 ms) groups than for the exclusive‐select (M = −36 ms) and exclusive‐reject (M = −30 ms) groups.

FIGURE 6.

Reaction time differences between responses to equivalence‐property tests and N‐ and N+ tests for the four groups. Black bars show the average differences in reaction times between responses to trials of equivalence‐relation tests and N‐ trials. The gray bars show the average differences in reaction times between responses to trials for equivalence tests and N+ trials.

*p < .05; **p < .01; ***p < .001.

Significant differences were observed between the differences in reaction times to equivalence test trials and N− and N+ trials, F(1, 316) = 37.571, p < .001, η² = 0.037. Significant differences were also observed between the four groups, F(3, 316) = 4.069, p = .007, η² = .024. Holm's post hoc analysis revealed significant differences between reaction times in the exclusive‐select group and the standard‐MTS, t(21) = −2.870, p = .026, and detached‐MTS, t(21) = −2.839, p .026, groups. No significant differences were observed in the interaction between differences in N− and N+ trials and the four groups, F(3, 316) = .989, p = .398, η² = .003. Holm's post hoc analysis revealed differences between differences to N− and N− trials in the standard‐MTS group, t(22) = 3.355, p = .021, the detached‐MTS group, t(20) = 3.351, p = .021, and the exclusive‐select group, t(21) = 3.861, p = .004. There were statistical differences between differences to N− trials in the exclusive‐select group and differences to N+ trials in the standard‐MTS group, t =(21) 5.289, p < .001, the detached‐MTS group, t (20) = 5.258, p < .001, and the exclusive‐reject group, t(21) = 3.064, p = .048. Finally, there were differences between differences to N− trials in the exclusive‐reject group and differences to N+ trials in the standard‐MTS group, t (22) = 3.605, p = .008, and the detached‐MTS group, t(21) = 3.609, p = .008.

DISCUSSION

The purpose of this study was to determine whether the type of conditional control associated with the formation of equivalence relations using the standard‐MTS procedure is exclusively based on select control or involves both select and reject control. As this cannot be directly determined through typical equivalence tests, equivalence trials were conducted using novel stimuli to replace either the incorrect stimulus (N−) or the correct stimulus (N+). The performance of participants trained with the standard‐MTS procedure was compared with those trained on conditional relations based exclusively on select control, reject control, or both (detached‐MTS group). Performance on N− and N+ tests served as an indirect indicator of what was learned in each group. Additionally, the analysis by Carrigan and Sidman (1992) allowed for precise predictions about how participants would perform on these tests based on the type of training, as outlined in Table 1.

Most predictions based on Carrigan and Sidman (1992) were confirmed for the N− test but not for the N+ test. Most participants across all groups showed consistent performance on the N+ tests, revealing the stimulus control underlying the different training types. The tendency of participants in the exclusive‐select and exclusive‐reject groups to respond to either the baseline stimulus or the novel stimulus, respectively, suggests strong control by the familiar stimulus while reflecting the stimulus control topography associated with each training type. This pattern aligns with the performance observed on N− trials. However, control by the familiar stimulus on N+ trials resulted in performances inconsistent with the formation of equivalence relations, as participants responded using the learned topography to stimuli belonging to the opposite class, as defined preexperimentally. This inconsistency was observed even among participants in the exclusive‐select group who met the equivalence class formation criterion.

In contrast, participants in the detached‐MTS group exhibited differential performance on N− and N+ trials. On N− trials, they showed a selection stimulus control topography for the familiar stimulus belonging to the same class as the sample. On N+ trials, they exhibited a reject response topography for the familiar stimulus belonging to a class opposite from the sample. This performance is consistent with the formation of exclusive and well‐defined stimulus classes. Moreover, this group demonstrated the highest probability of equivalence‐relation formation, contrary to the predictions based on Carrigan and Sidman (1992). These results align with Stromer and Osborne's (1982) analysis of equivalence emergence and other studies showing equivalence under high select and reject control (e.g., Arantes & de Rose, 2015; Carr et al., 2000; de Rose et al., 2013; Grisante et al., 2014; Harrison & Green, 1990; Kato et al., 2008; Plazas, 2019, 2024; Plazas & Peña, 2016; Plazas & Villamil, 2016, 2018). Participants in the standard‐MTS group displayed more variable results on the N+ test but were generally more like the detached‐MTS group. Additionally, the performance on N− and N+ tests by participants who met the equivalence emergence criterion, along with differences in correct responses and reaction times, suggests that the behavioral mechanisms underlying equivalence relation formation in the standard‐MTS group are more frequently associated with those of the detached‐MTS group than with those of exclusively selection‐based conditional relation acquisition.

Meeting the criteria in equivalence‐select tests appears to mask two different behavioral mechanisms: one based exclusively on select control and another on combined select and reject control. These mechanisms produce different effects on N+ tests. According to the current results, exclusive select control cannot prevent performances inconsistent with the formation of exclusive and well‐defined classes. The same phenomenon occurs in the exclusive‐reject group. We suggest that this phenomenon be termed pseudoequivalence. In consequence, equivalence derived from exclusively select‐ or reject‐based conditional relations, as described by Carrigan and Sidman (1992) and supported by empirical evidence (Johnson & Sidman, 1993; Perez et al., 2015), constitutes pseudoequivalence. In contrast, stimulus equivalence emerging from combined select and reject control entails the formation of authentic equivalence classes. The results of this study suggest that participants trained with the standard‐MTS procedure may demonstrate pseudoequivalence or authentic equivalence, with the latter being more likely.

Accepting Sidman and colleagues' (Carrigan & Sidman, 1992; Johnson & Sidman, 1993) proposition that select and reject conditional control lead to the formation of alternative and incompatible equivalence classes raises the following question: How do these repertoires harmonize to enable authentic equivalence relations under the standard‐MTS procedure? The performance of detached‐MTS participants on N− and N+ tests suggests a potential answer. The standard‐MTS task involves reinforcement contingencies such that sample‐S+ and sample‐S− relations consistently control the same correct responses. Participants seem to acquire a repertoire of intraclass select relations and interclass reject relations during training (Plazas & Villamil, 2016). This repertoire generalizes to tests, allowing differential responses to intraclass and interclass sample–comparison relations, enabling mutual support between select and reject control. However, this repertoire appears complex and not directly derived from the conditional control acquired in training. To account for it, the participants' learning history may need to be considered. Plazas and Peña (2016) suggested that this history might involve the behavior of sorting stimuli into exclusive classes. Some studies suggest a relation between equivalence classes and sorting behavior (Fields et al., 2014; Fields & Reeve, 2001; Galizio et al., 2001). It is possible that this behavior is often accompanied by verbal strategies (Horne & Lowe, 1996; Randell & Remington, 1999; Wulfert et al., 1991), although authentic stimulus equivalence classes under the standard‐MTS procedure might also be achieved through a variety of strategies.

This study, however, presents some limitations. One major limitation is the difficulty in replicating the emergence of reject‐based equivalence despite using Carrigan and Sidman's (1992) procedure to bias control and Perez et al.'s (2015, 2019, 2020) procedure to direct attention toward the S−. Notably, the exclusive‐reject group experienced the greatest challenges in maintaining the baseline, with most reported test phases requiring reexposure. There were procedural differences between this study and others that observed reject‐based equivalence. For example, this study had a much higher proportion of test trials relative to baseline trials during the test phases. There were also differences in the stimuli that were used, and there was no verification that the stimuli lacked preexisting meaning for the participants. Additionally, the topography of reject control is presumably more complex than that of select control because it involves responding to a stimulus different from that which controls the response, and creating an effective attention bias toward reject relations remains a significant methodological challenge (Perez et al., 2019, Experiment 1; Plazas, 2024, Experiment 2). It is possible that this group benefited from more extensive training. Despite these challenges, participants' performances on reflexivity and transitivity/equivalence tests, when showing a reject‐equivalence pattern, were consistently accompanied by novel stimulus selection on both the N− test, as expected, and the N+ test. The latter performance suggests, by analogy with the exclusive‐select group, that reject equivalence may also produce a form of pseudoequivalence.

A major concern with the current study involves the use of tests with novel stimuli to assess baseline conditional control and performance on equivalence tests. Two main objections have been raised about such tests. First, participants may exhibit a preference for responding to novel stimuli (e.g., McIlvane et al., 1987; Stromer & Osborne, 1982). Second, the introduction of novel stimuli may inadvertently produce new learning during testing, thereby altering the conditional select or reject relations established during training (Carrigan & Sidman, 1992; Grisante et al., 2014; Kato et al., 2008). Regarding the first concern, preference for novel stimuli has been reported in both typically developing and intellectually disabled children (e.g., Valenti, 1985; Zeaman, 1976). In contrast, participants in our study appeared to exhibit a pattern of neophobia, which was particularly evident in the exclusive‐select group. Even the tendency of the exclusive‐reject group to respond to the novel stimulus in N+ tests seems explainable by baseline stimulus control with a reject‐type response topography. Therefore, it is not evident that participants in this study demonstrated any preference for novel stimuli.

With respect to the second concern, baseline conditional control was assessed in this study immediately after participants met the learning criterion and it was not reassessed later to examine changes across the testing phases. However, most participants across all groups exhibited response patterns in the N+ and N− tests that were consistent with the initial assessment of conditional control. Only a few participants in the exclusive‐reject group showed clear changes in conditional control, which were accompanied by corresponding effects on their responses in the equivalence tests. Nevertheless, it is unclear whether these changes were caused by the use of novel stimuli. One could argue that the effect of the novel stimuli occurred during the administration of the conditional control test and persisted throughout the subsequent phases. However, the results of the conditional control tests were characteristically distinct—particularly for the exclusive‐select, exclusive‐reject, and detached‐MTS groups—and aligned with expectations based on training. Thus, there is no evidence in this study of a change in baseline conditional control due to novel stimuli. Nevertheless, it is possible that such an effect occurred inadvertently due to the manner in which data were recorded. In this respect, there are alternative procedures for assessing conditional control, such as the use of a blank comparison stimulus, developed by McIlvane and colleagues (McIlvane et al., 1987), which attempts to avoid issues associated with novel stimuli and has been primarily employed to study the phenomenon known as exclusion learning (e.g., Plazas, 2021; Wilkinson & McIlvane, 1997). This procedure could be employed in future studies using a design similar to the present one.

Finally, one might argue that the higher probability of equivalence relation formation with the detached‐MTS procedure is a result of this group receiving more extensive training than the others. However, it is also true that the detached‐MTS group faced a more complex baseline that involved more stimuli and trial types than the other groups. The groups were equated in terms of learning criteria and retraining/retesting criteria. If the groups had been matched by the number of training trials, some participants would have received overtraining, which might have introduced other differences in test performance. Furthermore, the detached‐MTS procedure yielded a higher probability of equivalence‐relation formation than observed in Plazas (2024, Experiment 1). In that study, exclusive select and reject relations were trained using the same set of X stimuli rather than using different sets (W, X, Y, and Z) for each type of relation, as implemented by Johnson and Sidman (1993) and Perez et al. (2015, 2019, 2020). This factor appears to have facilitated the acquisition of select and reject conditional relations and the formation of equivalence relations.

The results of this study support the notion that although the conditional control acquired during training is necessary for the formation of equivalence relations, it is not sufficient. Other behavioral mechanisms, likely influenced by prior learning history, appear to be involved, but they remain unidentified. Unfortunately, most studies investigating the sources of control in the emergence of equivalence, including this one, have been conducted with typical adult human participants who possess extensive educational backgrounds. To identify the behavioral mechanisms underlying the emergence of equivalence using the standard‐MTS procedure, further research should focus on human participants with a significantly more limited learning history.

AUTHOR CONTRIBUTIONS

Elberto A. Plazas conceived and planned the study and carried out the experiments. Juan C. Forigua designed the computational program and analyzed the data. Elberto A. Plazas wrote the manuscript with the support of Juan C. Forigua.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

ETHICS APPROVAL

All procedures performed in studies involving human participants followed the ethical standards of the institutional research committee and with the 1964 Helsinki declarations, and its later amendments or comparable ethical standards. All participants in this study completed an informed consent form with the standard content for these types of studies.

Plazas, E. A. , & Forigua, J. C. (2025). Select and reject conditional control on matching to sample and stimulus equivalence. Journal of the Experimental Analysis of Behavior, 124(2), e70051. 10.1002/jeab.70051

DATA AVAILABILITY STATEMENT

The data set analyzed during this study is available in the figshare repository: https://doi.org/10.6084/m9.figshare.26132623.