Transformation of Thought Suppression Functions Via Same and Opposite Relations

The aim of this study was to investigate transformation of thought suppression functions via ‘same’ and ‘opposite’ relations. In Experiment 1 participants were given training and testing with the aim of generating same and opposite relational responding in two five-member relational networks. They then had to suppress a target word from one of the two networks, while words appeared individually onscreen including the target, and words either in the same (target) or a different (nontarget) network. They could remove any word by pressing the spacebar. Findings showed more frequent and faster removal of the target than other words and of words in the target network than other words. Experiment 2, the aim of which was to include predominantly ‘opposite’ relations in the relational networks, produced a similar but weaker pattern. Experiment 3 replicated the pattern seen in Experiment 2, while showing that the relations designated as opposite produced a more conventional transformation of functions in a context other than thought suppression.

1 Wegner (1989) drew a distinction between subtypes of thought control including suppression ("I will not think of X") and distraction ("I will think of Y"), and suggested that thought suppression more broadly conceptualized probably involves moving from the first to the second. Wegner's ECH focuses more on the second than the first and so does the current study. This can be justified as this is a particularly common strategy of thought suppression conceptualised more broadly (Rachman and de Silva 1978). In addition, the current study is an extension of previous work that was interested primarily in how derived relations impact on thought suppression than on modelling the phenomenon itself completely. those of Wegner et al., we will first provide a brief description of thought suppression from the current perspective.
From a contextual behavioral point of view, 'thinking' is a type of verbal behavior. RFT sees the latter, in turn, as a form of generalized relational responding referred to as relational framing (see Dymond and Roche 2013 for recent empirical data supporting this approach). From this perspective, relational framing, including thinking, is part of an individual's learned behavioral repertoire and, as with other forms of behavior, it can itself become a stimulus that evokes or elicits further responding, including (very often) further relational framing. Thought suppression is one such pattern of behavior that occurs in response to one's own previous framing. It can be conceptualised specifically as coming under the influence of a relational network or 'rule' of the form 'Do not think of X' (see Wilson et al., 2001). In a naturalistic context, X might be the name of something unpleasant or aversive. In any event, however, this particular type of rule is unusual. From an RFT point of view, relational framing in accordance with a rule typically transforms the functions of the environment for a verbal listener such that they respond to it in particular ways as specified by the rule. For example, the rule "Stay on the path" may strengthen the approach functions of the path referred to in the rule. However, in the case of the rule 'Do not think of X, ' the relational behavior specified is incompatible with the relational behavior involved in understanding the rule in the first place. More specifically, understanding the rule involves thinking of (framing with respect to) X; however, this is behavior that the rule itself proscribes. Hence, following the rule is impossible.
Nevertheless, behavior can still be affected by this rule because the listener might derive relations based on it, such as 'Well, if I'm supposed to not think of X, then I should try to think of something other than X.' Wegner's ECH theory provides a cognitive interpretation of the psychological processes that ensue. Following this rule will likely involve coming under the stimulus control of an object or event that is in a relation of being different from or in opposition to the target (to-be-avoided) stimulus for the rule follower. That might happen through physical orientation to objects/events that are framed as being in such relations in the immediate environment, or by responding covertly to stimuli or events that are thus framed and not immediately present.
This 'distraction' strategy might be understood as a type of self-control strategy. In the behavioral literature, self-control has been interpreted in terms of manipulation of one's environment in order to bring one's behavior under appropriate control (e.g., Lattal 2012). For example, attempted selfcontrol over drinking might involve goal setting (e.g., zero or a reduced number of units to be drunk this week), stimulus control (e.g., removing bottles of alcohol from ones environment), self-monitoring (e.g., checking how much alcohol has been consumed recently), rewarding goal attainment (e.g., self-praise or provision of tangible reinforcement for compliance), etc. (see e.g., Hester 1995). Attempted thought suppression might be characterised in a similar way. In this case also, self-control techniques might be utilised. Distraction, for example, might be thought of as a form of attempted stimulus control that might make thinking the unwanted thoughts less likely. It might work to some extent if after engaging in it for a period of time the person is no longer relationally framing with respect to the 'to-be-avoided' stimulus; if, in other words, they are no longer 'conscious' of the target. While distraction might work analogous to the above example, however, one key problem with thought suppression comes with the component of self-monitoring. In this case, to check if they are following the rule, the person must periodically compare the behavior specified by the rule (i.e., 'Do not think of X') with their own recent behavior. Doing this involves relationally framing in accordance with the rule again, which means framing with respect to (and thus becoming conscious of) the target again and, thus, immediately breaking the rule again. Consequently, checking the success of the attempt necessitates breaking the rule. In an important sense, then, true thought suppression seems self-contradictory and impossible.
Despite this, there is a sense in which attempted suppression may be evaluated by the person engaging in this behavior as successful to at least some extent and to be more successful on some occasions than on others. Length of time during which a person has not been relationally framing with respect to a suppression target may be one important variable regarding the evaluation of success. If the person does not frame with respect to the 'to-be-avoided' stimulus for what they discriminate as a sufficiently long time, then when they next compare their behavior with the rule they may judge the former as relatively successful with respect to the latter. Conversely, the shorter the period during which they have not been framing the target, the less likely the person may be to say that they have been successfully suppressing. Certain stimuli, including environmental stimuli, as well as a person's own relational framing, may make the 'period of successful suppression' shorter than it otherwise might be. One subcategory of such stimuli, identified by Wegner, that might do this could be stimuli framed as distractors. As discussed above, these stimuli might have been originally framed as being in a relation of being different from or in opposition to the to-beavoided stimulus. However, despite the nature of the relations involved, the very fact that they are relationally framed with the stimulus means that they may now be more likely to evoke the stimulus (just as 'white' might evoke 'black,' for example). It is possible that the more frequently particular distractors are involved in suppression behavior, the stronger the relation between them and the to-be-avoided stimulus, such that the more likely those distractors will be to cue the 'to-be-avoided' stimulus. In addition, the greater the number of different distractors involved, the greater the chances of evocation of the 'to-be-avoided' stimulus also.
So far, the contextual behavioral RFT explanation can be seen as simply paralleling the cognitivist explanation, given earlier by Wegner and colleagues, for why suppression is so often unsuccessful. However, the RFT approach can also extend Wegner's conceptualization. According to RFT, the learned human capacity to relationally frame stimuli allows humans to demonstrate derived relational responding (DRR). Furthermore, evidence provided by Hooper et al. (2010) indicates that this phenomenon may play a critically important role in making thought suppression unsuccessful.
The most well-known example of DRR is stimulus equivalence. This is an empirical effect in which an experimental participant is taught a series of interrelated conditional discriminations between arbitrary stimuli and subsequently derives an equivalence (sameness or coordination) relation between the stimuli involved. For example, when a verbally able human is taught to select stimulus B in the presence of stimulus A and to select stimulus C in the presence of B, then they are likely to derive a relation of sameness between A, B, and C and, thus, if tested will show a number of additional untrained performances on this basis (e.g., selection of A in the presence of B and B in the presence of C [symmetry]; selection of C in the presence of A [transitivity]; and A in the presence of C [combined symmetry and transitivity]). In addition, equivalence is accompanied by a 'transfer of function' effect, whereby a psychological function trained to one member of an equivalence relation spontaneously transfers to the other members without additional training (Auguston and Dougher 1997;Barnes et al. 1995;Greenway et al. 1996;Roche and Barnes 1997). For example, in Auguston and Dougher (1997), participants trained to avoid a stimulus paired with shock also showed avoidance of stimuli in derived equivalence relations with the conditioned stimulus. Hooper et al. (2010) showed how the phenomenon of transfer of function through derived equivalence relations could make thought suppression less successful (i.e., as per our discussion above, of relatively shorter duration). These authors referred to the phenomenon whereby certain stimuli could make thought suppression less successful by functioning as 'interference' with thought suppression. In addition, they argued that the process described by Wegner's ECH (whereby a stimulus directly framed by the participant as a distracter could eventually result in less successful suppression) should be designated 'direct' interference, while the process of making suppression less successful based on derived relations should be designated 'indirect' interference. In this study, participants were first trained and tested for the derivation of three three-member equivalence relations. They were then instructed to suppress all thoughts of a particular target word that had appeared in one of the three derived equivalence relations. While trying to suppress the target word, they were given the option to remove words that appeared on a computer screen. These words included the to-besuppressed target stimulus, as well as words that were directly trained to this stimulus (i.e., words whose selection in the presence of the target stimulus was reinforced) and words that were in derived relations with it. As in previous paradigms used by Wegner and colleagues, removal of a word was treated as indicating that that word interfered with thought suppression. Findings showed that, as expected, based on previous empirical work, the participants removed the target word as well as words that were directly trained to this stimulus; however, in addition, they also removed words in derived relations with the target. In removing the target and words directly trained to the target, participants showed direct thought suppression interference. However, in removing words in derived relations with the target, they also showed indirect thought suppression interference via derived transfer of function.
Thus, Hooper et al. extended the research of Wegner and colleagues by showing that derived equivalence responding might constitute a process whereby indirect thought suppression interference could occur. This was an important advancement; however, according to RFT, humans show many patterns of DRR in addition to equivalence. These include opposition, distinction, comparison, and deixis, for example, and there is by now an appreciable quantity of empirical evidence for them (see Dymond and Roche 2013). As such, it seems likely that promulgation of thought suppression through nonequivalence relations could also be possible.
A recent study by Dymond et al. (2007) provides an example of the empirical demonstration of derived relations other than equivalence. In this study, nonarbitrary relational training was first provided to establish arbitrary shapes as contextual cues for patterns of 'same' and 'opposite' relational responding. In the presence of one arbitrary shape (designated 'same'), participants were trained to choose comparison stimuli physically identical to a sample (e.g., short lineshort line), while in the presence of a second shape (designated 'opposite'), they were trained to choose comparison stimuli as physically different from the sample as possible (e.g., short linelong line). Once thus established, the cues were then used to train patterns of same and opposite relations between arbitrary nonsense syllables. and C1 are the same as each other. Furthermore, having been trained that C1 is the same as A1 and B2 is the opposite of A1, they derived that C1 and B2 are opposite. Finally, having been trained that both B2 and C2 are opposite of A1, they derived that they are the same as each other.
More importantly from the perspective of the current study, these researchers also demonstrated a transformation of functions in accordance with both same and opposite relations. 'Transformation of functions' is an RFT term used to refer to the acquisition by a stimulus of a novel psychological function or functions in the absence of direct training, based on the participation of that stimulus in derived relations. In the context of equivalence, the term 'transfer of function' can be used because the novel functions that are acquired by stimuli in derived equivalence relations with the originally trained stimulus are the same as the originally trained functions. However, in the context of multiple derived stimulus relations, including nonequivalence relations, the more generic term 'transformation of functions' is preferred because the functions that are acquired can differ from those originally trained, depending on the nature of the derived relations in question. 2 For example, if a relation of opposition is derived between two stimuli A and B, and A has previously been trained to be discriminative for avoidance, then the functions of B may be transformed such that B becomes discriminative for approach. Dymond et al. (2007) examined derived relations-based behavioral change involving the same psychological function as in Augustson and Dougher (1997), namely a shock avoidance function. Just as in the latter study, participants in the former study were trained to make an avoidance response in the presence of one particular stimulus (B1). However, whereas Auguston and Dougher (1997) showed transformation of avoidance functions in accordance with equivalence or sameness relations exclusively, Dymond et al. (2007) showed transformation of avoidance via both sameness and opposite relations. For example, all but one of the participants who showed conditioned avoidance with B1 also showed transformation of C1 and C2 via sameness and opposition, respectively, so that C1 acquired an avoidance function while C2 acquired an approach function.
The purpose of this study was to extend Hooper et al. (2010) by assessing for transformation of thought suppression interference via sameness and opposition relations. In a context in which the psychological functions at issue are thought suppression interference functions, exploring transformation through relations of opposition is particularly interesting. First, opposition would seem relevant because when a person is trying to suppress a thought then one strategy may be to think of something that is the opposite of the to-be-suppressed stimulus along one or more pertinent dimensions. For example, if I am trying not to think of something sad or depressing then I may think instead of something that is the opposite in that it is typically happy or uplifting. However, if, as seems possible, this can fail, then what is happening under those circumstances is that stimuli previously supposed to be in opposition relations have acquired functions of the to-besuppressed stimulus. If the latter occurs then this would suggest that, at least in this context, a coordinate frame has been derived between the stimuli and transformation of functions via sameness. Thus, a second reason that (nominally) opposition relations seem particularly worthy of exploration in this context is this possible switching of contextual control that may result.
This study aimed to train and test same and opposite relational networks using a similar procedure to that employed by Whelan et al. (2005), a previous RFT-based study that investigated priming effects in networks of same and opposite relations. In Experiment 1 of the current study, a nonarbitrary relational training and testing procedure was first used with the aim of establishing contextual cue functions in arbitrary shape stimuli. Next the contextual cues were employed with the aim of training and testing two separate arbitrary relational networks, both involving arbitrary nonsense syllables in both trained and derived same and opposite relations. Then, using a procedure similar to that employed in Hooper et al. (2010), participants were required to suppress a target word from one of the two relational networks. In the final phase of the procedure, participants were given the option to remove words that appear on a computer screen. These words included the to-be-suppressed target, words directly trained to it, words in derived same and (nominally) opposite relations with it, and words from the other relational network (i.e., the one not including the target word). Direct and indirect (derived) thought suppression interference was measured by assessing both frequency and latency of word removal and comparisons across nominally different word categories. As in Hooper et al. (2010), the latency of word removal was included as an alternative measure of responding that might yield additional information concerning response patterns. Though in Hooper et al. (2010) no detectable difference was seen between latency and frequency in terms of the broad pattern observed, the latter were analysing derived thought suppression in the context of equivalence only. In the context of the analysis of both 'same' and (nominally) 'opposite' relations it is possible that latency might pick up on differences between the relations that frequency does not.
We predicted that, as in similar previous RFT studies, there would be a change of stimulus functions via derived relations. For participants showing a typical transformation of functions through opposition, a pattern in the final phase whereby they acted to increase the frequency of the appearance of stimuli in opposition relations with the target stimulus or extend the length for which they were displayed might be predicted, at least in theory. In the present set-up, these actions were not actually possible, but at least deliberate inaction was. However, as indicated, we predicted that the change of functions through the (nominally) opposition relations might be different (and more specifically, more similar to that seen for equivalence relations) when tests for function transformation were conducted in the context of thought suppression than in the context of other functions, such as shock avoidance.

Participants
Eleven individuals participated in the study. Of these, 3 were female and 8 were male and their ages ranged from 22 to 30 years (M=25.3). All participants were volunteers who were contacted through personal acquaintances and chosen on the basis that they had no previous experience or knowledge of derived relations.

Design
We conducted both single subject and group analyses. For the latter, we employed a within subjects design with repeated measures taken on word relation type (target, taught same, derived same, derived opposite, nontarget network, non-network, novel). The two dependent variables were frequency and latency of word removal.

Apparatus & Materials
Experiments were conducted in a small room in which participants sat at a table with a computer programmed in Visual Basic 6.0 that controlled all stimulus presentations and recorded all responses. Two arbitrary stimuli were established as contextual cues for Same (i.e., ♑) and Opposite (i.e., ♓), respectively. The stimuli used in the relational networks and in the suppression phase in Experiment 1 and subsequent experiments are shown in Table 1. The alphanumeric labels in brackets beside the stimuli used during the training and testing of the relational networks are employed in this report for ease of communication. The participants never saw these labels.

Procedure
We exposed participants to the following five experimental phases:   This phase involved nonarbitrary relational training and testing using a matching-to-sample (MTS) procedure. On each trial, the arbitrary shape to be established as a contextual cue appeared first after 0.5 seconds in the top centre of the computer screen, then 0.5 seconds later the sample stimulus appeared in the middle of the screen and finally another 0.5 seconds later three comparison stimuli appeared in a quasi-random positional order of presentation along the bottom. Stimuli remained on the screen until the participant selected one of the comparisons using the mouse. During training, feedback ("Correct" or "Wrong") was presented in one-inch-high red letters in the centre of the screen for 1.5 s. During testing, no feedback was presented. An inter-trial interval of 2.5 s followed the feedback during training and the response during testing.
The sample and comparison stimuli in both training and testing were related to each other along a physical dimension and the correct answer depended on the contextual cue and the nature of the physical relation. For example, in the case of one set of stimuli, the sample was either a short line or a long line and the comparison stimuli consisted of three lines; long, medium, and short. If the contextual cue for same was presented, then a correct response involved choosing the comparison that was the same length of line as the sample, while if the contextual cue for opposite was presented then a correct response involved choosing the short line if the sample was long and vice versa.
We use the following convention in describing match-tosample probes, both non-arbitrary and arbitrary: The contextual cue is presented first, followed by the sample stimulus and then the three comparisons are listed in brackets with the reinforced comparison in italics. Using this convention, the trial types described in the last paragraph are as follows: SAME . This collection of trial types constitutes one problem set, referred to as Problem Set 1. There were four problem sets in total, each utilizing different stimuli (lines, shades, clouds, and cubes) and each consisting of four trial types analogous to those in the first set. The trial types for each problem set were presented in a quasi-random order in blocks of four trials with each trial-type presented once per block. During the first training phase participants were trained on alternate blocks of Problem Set 1 and Problem Set 2 trials with each block presented four times, making a total of 32 trials, and they were required to respond correctly to each of the final 16 trials in order to reach the mastery criterion.
If a participant did not reach the mastery criterion, then we exposed them to another 32 trial phase on Problem Sets 1 and 2. If they did reach the criterion, then they received the first nonarbitrary relational testing phase. This was similar to the training phase in that it involved alternating blocks of quasirandomly ordered trial-types. However, during this phase there was no feedback and Problem Sets 3 and 4 were used instead of Sets 1 and 2.
(ii) Same & Opposite Arbitrary Relational Training and Testing. Nonarbitrary relational training and testing was immediately followed by arbitrary relational training and testing. This used the contextual cues established in the previous phase to train and test two separate networks of arbitrary same and opposite relations using mostly nonsense words as stimuli but also including two real words, one assigned to an experimental network ('Bear') and one assigned to a control network ('Shoe').
Instructions and the MTS procedure were similar to the previous phase. This phase involved two separate stages. Both involved training and testing two separate relational networks including a target network that contained the word (Bear) to be used as the to-be-suppressed (target) word in the latter phase of the experiment, and a nontarget network (see Fig. 1 for the two networks and Table 1 for the stimuli used). However Stage 1 focused primarily on the target network while Stage 2 focused primarily on the nontarget network.
Stage 1. This stage involved the following eight training-trial types (the correct choice is in  Table 1) in the target (left) and nontarget (right) relational networks in all three experiments. In Experiment 1, the 'to-be-suppressed' word was B1 while in Experiments 2 and 3, it was B2 italics; see Table 2 The latter 4 tasks involved stimuli from the nontarget network but they functioned primarily to support the training of the target network by ensuring that participants were not simply being taught to always pick B1 and C1 in the presence of SAME and always pick B2 and C2 in the presence of OPPOSITE, which would be inappropriate stimulus control. Training was presented in quasi-random blocks of eight trials in which each of the above trial types was presented once and were repeated until the participant had responded correctly to forty consecutively correct trials. Once the criterion had been met, the testing section began. The aim of arbitrary relational testing was to assess for responding in accordance with the derived relations of SAME and OPPO-SITE in each of the two networks, as per Fig. 1. In the target network, the testing-trial types were as follows (see Table 2): . Given the relations that were trained, participants were expected to make the following selections: (i) C1 with B1 in the presence of the SAME cue (because both are the same as A1); (ii) C2 with B2 in the presence of SAME (because both are opposite to A1 and, thus, the same as each other); (iii) C2 with B1 in the presence of OPPO-SITE (because B1 is the same as A1 and C2 is opposite to A1 thus B1 is opposite to C2); (iv) C1 with B2 in the presence of OPPOSITE (because B2 is the opposite to A1 and C1 is the same as A1 so therefore B2 and C1 are opposites). Testing involved the quasi-random presentation of the 4 trials types 8 times each in a block of 32 trials. The mastery criterion for passing the testing was 31/32 correct responses. If the participant passed, then they were exposed to Stage 2 of training and testing (i.e., focusing on the nontarget network).
If they failed then they were re-exposed to Stage 1 training and testing up to a maximum of four times, after which, if they had still not passed, they were excused from further participation in the experiment. Stage 2. Training for this stage involved the following eight trial-types: Table 2). Testing involved the following four trial types: Given the relations trained, participants were expected to make the following selections: (i) Z3 with Y3 given SAME; (ii) Z4 with Y4 given SAME; (iii) Z4 with Y3 given OPPOSITE; (iv) Z3 with Y4 given OPPOSITE. Testing involved the quasirandom presentation of the 4 trial types 8 times each in a block of 32 trials. The mastery criterion for passing the testing was 31/32 correct responses. If the participant passed, then they were exposed to the next session of training and testing, and if they failed, they were then re-exposed to training and testing for the nontarget network up to a maximum of four times, after which, if they had still not passed, they were excused from further participation in the experiment. If a participant passed training and testing in both the target and nontarget networks, then they graduated to the suppression induction phase. (iii) Suppression Induction. The aim of this phase was to familiarise participants with the suppression task. It began with the participant being instructed to suppress all thoughts of the word 'Bear' for a five minute period.
The following onscreen instruction was presented: "For the next phase of the experiment, try not to think of the word 'Bear'. If you have any questions, please ask the experimenter." Once the participant had read this instruction, then, if they had a question for the experimenter, then he would repeat the relevant instruction. After this, or if they had no questions, they could continue by clicking a button that produced the next instruction: "For the next five minutes you have to press the spacebar every time you think of the word 'Bear'.
Press the 'Continue' button when you are ready to begin." Once the participant had pressed the 'Continue' button, the screen went blank and it remained blank for five minutes. During this time, the task of the participant was to suppress thoughts of the word 'Bear' and to press the computer spacebar every time they thought of the word. (iv) Cognitive Load Induction. The purpose of this brief penultimate stage of the experiment, which followed immediately after the suppression induction stage, was to provide the participant with a 'cognitive load' that would be present during the suppression task, because evidence suggests that having a relatively high cognitive load increases the rebound effects of attempted thought suppression. Participants saw the following instruction across the middle of the computer screen: "Thank you for your participation so far. Next, you are about to see a 9-digit number. Your job is to commit this number to memory over the next 25 seconds and write it down at the end of the experiment. Press the 'Continue' button to see the number." When participants pressed the continue button, they saw a nine digit number, which remained on the screen for twenty five seconds.
(v) Suppression Task. This final stage began immediately after the end of the cognitive load induction. The participant was presented with the following instructions: "For the next part of the experiment you are asked to continue to suppress the thought you have been asked to suppress whilst attending to the computer screen. It is important that you continue to suppress this thought as you did in the previous part of the study. Once the program has started, words will appear every ten seconds in the centre of the screen. However, you are in control of the program, so, if you are not happy with a word being on the screen then you can remove it by pressing the spacebar. If you choose to remove a word the screen will stay blank for the remainder of the 10 seconds at which point the next word will appear. Remember that it is vitally important that you attend to the screen but continue to suppress the thought. When you are ready, please press 'Continue'." During this phase, a set of 28 words in quasi-random order was presented on the computer screen four times in succession, making a total of 112 word presentations. The set of words included the words, both nonsense and real, that were in the two trained and tested relational networks as well as other, previously unseen words (see Table 1). Each word was presented onscreen for ten seconds. Removal of a word meant that the screen remained blank for the remainder of the ten seconds before the next word was presented. Because each word was presented four times, participants had four opportunities to remove each word. The computer program recorded how many times each word was removed, and, in the case that a word was removed, the latency from the stimulus-onset to the removal of the word. After completing the suppression task, participants were thanked and fully debriefed.

Experiment 1: Results & Discussion
All eleven participants passed nonarbitrary relational training and testing on their first attempt. One person (male, age 22) failed to pass arbitrary relational testing for the target relational network and was excused. The remaining ten completed two sessions of arbitrary relational training and testing (i.e., one for the target network and one for the nontarget network), with none taking more than three cycles of training and testing to reach the criterion in either session. All ten showed space bar presses (M=30.7, range=7-76) during the 5-minute suppression induction phase and at the end of the experiment, all correctly reproduced the 9-digit number from the cognitive load phase, showing that they had followed the instructions for the latter. Figure 2 shows the mean frequency of removals for seven word categories in the suppression task (separate analyses suggested no significant differences in responding to B2 and C2, the stimuli in derived opposite relations with the target and, thus, their data were combined): (a) the target (M=4.00, SD=0.00); (b) the trained SAME word (M=3.1, SD=1.52); (c) the derived SAME word (M=3.00, SD=1.33); (d) the mean of the two derived OPPOSITE words (M=2.7, SD= 1.57); (e) the mean for nontarget network words (M=1.32, SD=0.96); (f) the mean for non-network words that appeared in training but were not part of either network (M=0.825, SD=1.33); and (g) the mean for novel words that appeared only in the suppression task (M=0.67, SD=1.19).

Suppression Task Word Removal Frequency
A one-way repeated measures analysis of variance (ANOVA) revealed a significant effect of word category, F(6, 54) = 11.851, p<.001, η p 2 =.568. The results of pairwise comparison t-tests (LSD) are shown in Table 3. The mean number of responses to the target was significantly higher than to all other categories except for the word in a trained relation of sameness, while the mean number of responses to all categories in the target network was significantly higher than to all categories outside the target network (i.e., nontarget network, non-network, and novel). This suggests that participants were significantly more likely to remove the target and words related to the target than words in an alternative relational network, or words that were unrelated or novel.
These group level results reveal a pattern in which participants responded strongly to avoid the 'to-be-suppressed' word and were also more likely on average to remove words related to that word, whether in relations of sameness or of opposition, than to remove words from outside that relational network. Most relevant for this study, there was no significant difference between mean number of responses to derived Fig. 2 Mean frequency of word removal responses made during the final (thought suppression) phase in Experiment 1 for seven word categories. The first four are word categories in the target relational network: 'Target' (B1), the 'to-be-suppressed word'; 'Same T' (A1), the word in a trained 'same' relation with the target; 'Same D' (C1), the word in a derived 'same' relation with the target; and 'Opp D' the mean for the two words (i.e., B2, C2) in a derived 'opposite' relation with the target. The remaining three are word categories from outside the target relational network: 'NT Net' is the mean for words in the 'Nontarget' relational network (X3, Y3, Z3, Y4, Z4); 'Non-Net' is the mean for words in arbitrary relational training and testing that were not part of either established network (N1, N2, N3, N4); and 'Novel' is the mean for words that did not appear during training and testing. Bars show standard error OPPOSITE (B2 and C2) words and the mean number of responses to the derived SAME (C1) word, though the mean number of responses to each of these was significantly higher than to nontarget network, non-network, and novel words. This suggests that the thought suppression functions of the target B1 was transformed to the same extent across both nominally SAME and nominally OPPOSITE derived relations. Figure 3 shows frequency of removal for each of the seven word categories in the target network (i.e., target, trained same, derived same, derived opposite, nontarget network, non-network and novel) for each individual participant. As may be seen, all participants removed the target the maximum number of times. In a number of cases (P2, P3, P5, and P9), all words in the target network were also removed the maximum number of times and there is a general trend whereby participants removed words in the target network more often than they removed words in other categories, indicating transformation of function. In a number of cases (P1, P4, P6, P7, P8, P10) there was a transformation of function of nontarget members of the experimental relational network, but not equally across all members; for example, in a number of cases (P1, P7, P8, P10), there was weaker transformation for one or more of the derived relations than for the trained relation. Figure 4 shows the mean response latency (in seconds) for seven word categories in the suppression task (analyses suggested no differences in responding to B2 and C2, the stimuli in derived opposite relations with the target and, thus, their data were combined): (a) the target (M=1.29, SD=0.30); (b) the trained SAME word (M=3.78, SD=3.41); (c) the derived SAME word (M=3.91, SD=2.73); (d) the average of the two derived OPPOSITE words (M=5.41, SD=2.78); (e) the mean for nontarget network words (M=7.67, SD=1.71); (f) the mean for non-network words that appeared in training but were not part of either network (M=6.05, SD=2.25); and (g) the mean for novel words that appeared only in the suppression task (M=8.85, SD=2.31).

Suppression Task Word Removal Latency
Data were analysed using a one way repeated measures ANOVA with the word category as the 'within subjects' factor. Mauchly's test indicated that the assumption of sphericity had been violated (χ 2 (20) = 33.882, p=.04) and, thus, degrees of freedom were corrected using Greenhouse-Geisser estimates of sphericity (ε=0.383). There was a significant effect of word category, F(6, 54) = 16.231, p < .001, η p 2 =.643. The results of pairwise comparison t-tests (LSD) are shown in Table 4. The pattern for removal latency was the same as for frequency. The mean latency for the target was significantly lower than that for all other categories except for the word in a trained same relation, and the latency for all categories in the target network was significantly lower than that for all categories outside the target network (i.e., nontarget network, non-network, and novel). This suggests that, as expected, participants were quicker to remove the target and words related to it, than to remove words in an alternative relational network, or words that were unrelated or novel. Thus, group level results reveal a pattern in which participants responded quickly to avoid the 'to-be-suppressed' word and were also faster on average to remove words related to that word, whether in nominal relations of sameness or of opposition, than they were to remove words from outside that relational network. With respect to words in the target network, responding was fastest to the target but there were no differences between the mean latencies of the other word categories, once more suggesting comparable transformation of function across derived relations regardless of the nature of the training contingencies (i.e., SAME or OPPOSITE). Figure 5 shows latency of removal for each of the seven word categories in the target network (i.e., target, trained same, derived same, derived opposite, nontarget network, non-network, and novel) for each individual participant. As may be seen, the target was generally removed faster than any other word category. In a number of cases (P1, P2, P3, P5, P8, P9), all words in the target network were removed faster than other word categories, while in other cases (P4, P7) almost all were removed faster. This general pattern thus suggests transformation of function within the target network.

Summary & Discussion
The core findings from Experiment 1 were that participants tended to (a) show strongest suppression responding to the target stimulus, and (b) show stronger responding to members of the target network, including words in both nominally same and nominally opposite relations with the target stimulus, than to words in other categories including nontarget network, nonnetwork, or novel. Assuming the efficacy of the thought suppression intervention early on in the experiment, finding (a) might have been predicted based on the fact that the target was the only directly conditioned stimulus, while finding (b) might have been predicted based on a combination of direct conditioning and transformation of function.
However, within the target network, we found no difference in either frequency or latency of thought suppression responding between nominally same and nominally opposite relations. The change in stimulus functions typically seen in  the context of opposition relations is qualitatively different from that seen in the context of sameness. Whereas the latter yields functions similar to those inhering in the original stimulus, the former often yields transformed functions that are contrary along specified dimensions to the functions of the original stimulus. For both of these reasons, if participants showed a typical transformation of functions through opposition, then a pattern whereby they acted to increase the frequency of appearance of the stimuli or extend the length for which they were displayed might have been predicted for stimuli in opposition relations. In the present set-up, these actions were not actually possible, but at least deliberate inaction with respect to these stimuli might have been expected. The pattern of action seen, whereby stimuli in both nominally same and nominally opposite relations with the target tended to be removed equally often and with similar latencies, defines the stimuli in the target network as having been in a relation of sameness when the test for function transformation was the suppression task. When the test for function transformation was the same-opposite arbitrary relational testing procedure (i.e., during Phase 2b), we observed function transformation in accordance with the nominally trained relations. However, when the test for function transformation was the suppression task, we observed function transformation consistent with a frame of sameness for all stimuli in the target network, running contrary to the nominally trained relations that were expected. Experiment 1, thus, appears to have demonstrated transformation of thought suppression functions via both nominally same and nominally opposite relations. This represents a replication and extension of Hooper et al. (2010) who provided the initial demonstration of transformation of thought suppression functions but who showed this effect via sameness relations alone. This experiment has additionally shown a transformation of function via nominally opposition relations. However, the function transformation for the nominally opposite relations were consistent with a frame of sameness. It was predicted that this might happen because the failure of thought suppression suggests that stimuli that are in a frame of opposition in some contexts are instead in a frame of sameness in the context of thought suppression. Now we have provided an empirical analogue of this process and have also shown once again the importance of contextual control with respect to derived-relations-based changes in response functions.
One arguable limitation of Experiment 1 was that it facilitated a relatively limited analysis of transformation of suppression function via opposite relations. For example, whereas the words in same relations with the target included a word in a trained same relation as well as a word in a relation that was based on the combination of two same relations, there were no words in a trained relation of opposition with the target nor any words related to the target via two relations of opposition. In order to provide a more thorough investigation of the change of functions via (nominally) opposite relations, a second experiment was conducted in which both these types of relation were included in the target relational network.

Experiment 2
The purpose of Experiment 2 was to allow for a more thorough investigation of transformation of thought suppression functions via derived opposition relations. It was similar to Experiment 1 in most regards. However, it differed in one key respect which was that the target stimulus (which remained the word 'Bear') occupied a different position in the target relational network such that a different set of trained and derived relations would be predicted to emerge and a different set of corresponding changes in thought suppression functions could be tested. More specifically, the target word (i.e., 'Bear') occupied the B2 position (see Fig. 1) and thus was trained as 'opposite' to the hub word (i.e., A1) and would be predicted to be in a derived relation of opposition with B1 and C1, and in a derived relation of sameness (via two opposition relations) with C2.

Participants
Eleven individuals participated in the study. Of these, 6 were female and 5 were male and their ages ranged from 17 to 50 years (M=32.1). All participants were volunteers who were contacted through personal acquaintances and chosen on the basis that they had no previous experience or knowledge of derived relations.

Design
As in Experiment 1, we conducted both single subject and group analyses. For the latter, we employed a 'within subjects' design with repeated measures taken on word relation type (target, taught opposite, derived same, derived opposite, nontarget network, non-network, novel). The two dependent variables were frequency and latency of word removal.

Apparatus & Materials
Most details were the same as in Experiment 1. However, the stimuli used in the trained and tested relational networks differed to some extent and, more importantly, the position of the target word 'Bear' within the relational network was changed (see Fig. 1 and Table 1).

Procedure
This was identical to that employed in Experiment 1.

Experiment 2: Results & Discussion
All eleven participants passed nonarbitrary relational training and testing on their first attempt. One person (male, age 21) failed to pass arbitrary relational testing for the target relational network and was excused. The remaining ten completed two sessions of arbitrary relational training and testing (i.e., one session for the experimental network and one for the control network), with no participant taking more than three cycles of training and testing to reach the criterion of 31/32 correct responses in either session. All ten showed space bar presses (M=35.6, range=5-156) during the 5-minute suppression induction phase and at the end of the experiment, and all correctly reproduced the 9-digit number from the cognitive load manipulation phase, indicating that they had followed the instructions for the latter. Figure 6 shows the mean frequency of removals for the following word categories in the suppression task (analyses suggested no significant differences between B1 and C1, the stimuli in derived opposite relations with the target and thus their data were combined): A one way repeated measures ANOVA revealed a significant effect of word category, F(6, 54) = 11.386, p<.001, η p 2 =.559. The results of pairwise comparison t-tests (LSD) are shown in Table 5. This shows the following: that the mean number of responses to the target was significantly higher than that to all other categories except for the word in a derived same relation; that the mean number of responses to the trained opposite word was significantly higher than that to all categories other than the target network; that the mean number of responses to the words in derived same and opposite relations was significantly higher than that to words in the non-network and novel categories; and that the mean number of responses to the words in nontarget and non-network categories was significantly higher than that to the novel words.

Suppression Task Word Removal Frequency
Overall, these group level results suggest, as in Experiment 1, that participants were more likely to remove the target and its related words than to remove words from other categories, suggesting transformation of function. However, the pattern for this experiment was not as strong or as clear cut as for the previous experiment. In particular, there did not appear to be as clear a distinction between the target network and the nontarget network in Experiment 2. Figure 7 shows the frequency of removal for each of the seven word categories in the target network (i.e., target, trained opposite, derived same, derived opposite, nontarget network, non-network, and novel) for each individual participant. As may be seen, all participants removed the target the maximum number of times. In a number of cases (P1, P2, P3, P5, P6, P10), all or all but one of the words in the target network also were removed the maximum number of times and there is a general trend whereby participants removed words in the target network more often than they removed words in other categories, suggesting that all words in the target network participated in a frame of sameness with the target during the suppression task. However, as suggested before, the pattern of acquisition of functions for members of the nontarget relational network seems comparatively stronger in this experiment than in the previous one. For example, in this experiment, there were four participants (P1, P2, P9, P10) who appeared to show relatively strong acquisition of functions for the nontarget relational network. Data were analysed using a one way repeated measures ANOVA with word category as the 'within subjects' factor. Mauchly's test indicated that the assumption of sphericity had been violated (χ 2 (20) = 35.832, p=.025) and thus degrees of freedom were corrected using Greenhouse-Geisser estimates of sphericity (ε=0.492). There was a significant effect of word category, F(6, 54) = 11.934, p<.001, η p 2 =.570. The results of pairwise comparison t-tests (LSD) are shown in Table 6. The pattern for removal latency is similar to that for frequency. Results indicated the following: the mean latency to the target was significantly lower than that to all other categories; the mean latency to the trained opposite word was significantly lower than that to all categories other than to those categories in the target network; the mean latency to words in derived same and derived opposite relations was significantly lower than that to words in the non-network and novel categories; and the mean latency to words in nontarget and non-network categories was significantly lower than that to novel words.

Suppression Task Word Removal Latency
These group level results suggest that, as in Experiment 1, participants were faster to remove the target and words trained to be part of the same network than to remove words from other categories, suggesting transformation of function within the target network. However, again, the pattern is not as clear cut as for the previous experiment, with the key difference being there does not appear to be as clear a distinction this time between the target network and the nontarget network. Figure 9 shows latency of removal for each of the seven word categories in the target network (i.e., target, trained  , either all or all but one of the words in the target network were removed faster than words in other categories. However, in the case of a number of participants, words in the nontarget network were removed relatively fast also.

Summary and Discussion of Findings for Experiment 2
Key findings include the following: (a) participants tended to show strongest suppression responding to the target stimulus; (b) participants tended to show stronger suppression responding to members of the target network than to stimuli not in that network including non-network stimuli and novel stimuli; (c) participants tended to show stronger responding to words that had been involved in arbitrary relational training and testing but were not part of the experimental relational network (i.e., both nontarget and non-network) than to words that were previously unseen (i.e., novel); and (d) participants tended to show stronger responding to the target than to the word trained to it. It was also noted that, in contrast with Experiment 1, there was a lack of a consistent pattern of statistically significant differences between stimuli in the target relational network and stimuli in the nontarget relational network. While the latter was not a positive finding, it was a potentially important contrast with Experiment 1 and, as such, it will be referred to as finding (e). Finding (c) suggests the stimuli in the nontarget relational network and non-network stimuli might have acquired weak suppression functions. This might of course be a statistical artefact given the relatively low numbers used in these experiments. However, assuming that something more is at play, then another possible reason for this pattern might be the relative importance of opposition relations in the target relational network during the current experiment as compared with Experiment 1. This might also help explain finding (e). Perhaps the relative importance of opposition relations affected derivation in accordance with the relational networks involved, and, as a result, produced less of a clear cut difference between stimuli inside and outside particular relational networks.
In the case of finding (e), this may have been exacerbated by the fact that, due to the training of stimuli from the two networks alongside each other, it is possible that the two relational networks involved might function under certain circumstances as one large network. Under such conditions, it is possible that it is nodal distance (i.e., the number of stimuli in between two stimuli in a derived combinatorially entailed relation; see e.g., Fields et al. 1984) from the target rather than differences between distinctive networks that produces differences in levels of transformation of function. This could perhaps have also affected Experiment 1; however, because the relational networks in that case were based more on sameness than opposition, the differences between the networks may have been clearer and hence there was less transformation of the nontarget network. In the case of finding (c), the relative importance of opposition relations in the network might have meant less of a clear cut difference between stimuli inside the trained and tested relational networks and stimuli outside those networks and, thus, resulted in the latter becoming more apparently different from completely novel stimuli.
Furthermore, finding (d) might further support an explanation cast in terms of the effect of opposition relations in the relational network. This finding was that there was a significant difference in suppression functions between the target and the word trained to it. This difference appeared in Experiment 2 but not in Experiment 1 and the reason may have been the type of relation trained. In Experiment 1, the trained relation was a sameness relation whereas in Experiment 2 it was an opposition relation. Assuming once again, that this is not a statistical artefact, it is at least possible that the difference in the type of relation involved may have played a role.
Apart from the relatively greater influence of opposition relations in the relational network, another factor contributing to the difference in the pattern of results seen in Experiment 2 might, of course, have been processes described within Wegner's original ECH. Stimuli outside the trained and tested relational networks might have been responded to as 'different' from any of the stimuli within those networks and, thus, at least temporarily, as more effective distractors than stimuli inside the relational network. However, the very fact of such earlier established relations with the relational networks including the target might eventually have caused them to function less effectively as distractors than stimuli that would have been completely novel during the suppression phase.
In summary, Experiment 2 appears to have extended the results of Experiment 1 by demonstrating a transformation of thought suppression functions via trained relations of (nominal) opposition. However, in both experiments, and  Fig. 9 Mean latency of word removal responses made for seven word categories by each of the ten participants during the final phase in Experiment 2 particularly Experiment 2, stimuli outside of the target relational network, including members of a second unrelated (nontarget) network as well as non-network stimuli, appeared to show transformation of functions also. Some possible explanations for these patterns have been discussed. One criticism of both experiments reported so far is that, though they appear to have involved opposition relations, neither of them showed a typical pattern of transformation of functions through opposition. Of course, a key aim of the current work is to investigate whether, under certain circumstances, stimulus relations functioning as opposite in one context may produce sameness-consistent transformation of function in another, and more specifically, one involving derived thought suppression; however, in order to provide the clearest evidence that this is indeed the case, it seems important to show conclusively that the original relations produced are indeed relations of opposition and still result in a conventional pattern of transformation of functions in at least some contexts. That was the aim of Experiment 3.

Experiment 3
Experiment 3 aimed to extend the results of the previous two experiments. The latter appears to show transformation of function via relations of (nominal) opposition; however, as the pattern of transformation seen was consistent with sameness rather than opposition then one possible criticism might be that the relations demonstrated were not functioning as opposition relations at any stage. The aim of Experiment 3 was to investigate the possibility of showing a transformation of functions more appropriate to opposition alongside a more consistent sameness transformation of functions via these relations, thus demonstrating that the latter did function as relations of opposition in at least some contexts.
To do this, in Experiment 3 we first trained and tested participants such that discriminative functions of selecting along an auditory nonarbitrary dimension (i.e., selecting a button producing either 1, 2, or 3 electronically produced 'peals') were established in several textual stimuli including the word 'Bear'. Training these functions allowed the possibility of a transformation of functions of other stimuli subsequently established as participating in either 'Same' or 'Opposite' relations with 'Bear'. We then trained and tested participants for arbitrarily applicable relational responding in accordance with 'Same' and 'Opposite' before re-exposing them to the test for discriminative functions. If participants immediately showed the predicted changes in response functions, then we exposed them to the same thought suppression protocol as described in the earlier experiments. If not, we reexposed them to 'Same' and 'Opposite' relational training and testing. One other difference between this study and the previous ones was that in the current study we employed the Relational Completion Procedure (RCP; Dymond and Whelan 2010) as the relational training and testing protocol. We used this rather than MTS to expedite participant progress.

Participants
Ten individuals participated in the study. Of these, 3 were male and 7 were female and their ages ranged from 16 to 50 years (M=26.1). All participants were volunteers who were contacted through personal acquaintances and chosen on the basis that they had no previous experience or knowledge of derived relations.

Design
As in previous experiments, both single subject and group analyses were conducted. For the latter, a 'within subjects' design was used with repeated measures taken on word relation type (target, taught opposite, derived same, derived opposite, nontarget network, non-network, and novel). The dependent variables were frequency and latency of word removal.

Apparatus & Materials
The new function training stage included two novel nonsense stimuli: Sackol (X1), Wilfop (X2). In the training and testing of the relational networks, the stimuli used once again differed to some extent from the previous experiments but, importantly, the position of the target 'Bear' within the relational network was the same as in Experiment 2 (see Table 1).

Procedure
In this experiment, participants were exposed to a multiphase procedure as follows: (i) initial function training and testing; (ii) relational completion procedure (RCP) training & testing; (iii) follow-up function training and testing; (iv) suppression induction; (v) cognitive load induction; and (vi) suppression task.
Phase (i): Initial function training and testing.
In the training phase, participants were exposed to a MTS training format on each trial, of which one of three textual stimuli, either X1 ('Sackol'), B2 ('Bear'), or X2 ('Wilfop'), would appear as the sample in the screen centre. After the participant pressed the centre stimulus, the comparisons would appear. These were three red square stimuli that appeared consecutively in three randomly chosen corners of the screen, each accompanied by an auditory stimulus, either one chime, two chimes, or three chimes. Reinforcement ('Correct' in the screen centre) was contingent on choosing the 'one chime' square given Bear (B2), the two chime square given Sackol (X1), and the three chime square given Wilfop (X2).
After participants achieved 18 consecutively correct responses, the testing phase began. This involved exactly the same format but for the following: (i) instead of the quasi-random presentation of X1, B2, and X3 as samples, the sample array included A1 (Casors), B2 (Bear), C2 (Vartle), B1 (Lorald), and C1 (Heiter); (ii) each sample was presented three times in a quasirandom order to give a total of 15 trials; (iii) correct responding was counted as 100 % correct responses in accordance with the relational network to be trained and tested in the next phase (see Phases [ii] and [iii]); (iv) no consequences were provided. Because correct responding was predicted to require transformation of function in accordance with the trained and tested network in Phase (ii), it was predicted that participants would fail to show the correct responding in this phase. Phase (ii): Relational completion procedure (RCP) training & testing.
After participants finished Phase (i) testing, the experimenter initiated Phase (ii). At the start, the following instructions were presented onscreen.
Thank you for agreeing to participate in this study. You will be presented with a series of images or nonsense words on the top half of the screen from left to right. Then you will be presented with three images or nonsense words on the bottom of the screen. Your task is to observe the images or words that appear from left to right and drag one of these images or words from the bottom to the blank yellow square. Click and hold the mouse over the image or word to drag it to the blank square. To confirm your choice, click 'Finish Trial'. If you wish to make another choice, then click 'Start Again'. Sometimes you will receive feedback on your choices, but at other times you will not. Your aim is to get as many tasks correct as possible. It is always possible to get a task correct, even if you are not given feedback.
Clicking on a box at the bottom of the screen cleared the instructions and then three seconds later, stage one of the REP started.
Throughout the REP protocol, the screen was divided into two areas, with the top two thirds blue and the remainder grey (see Fig. 10). The sample appeared on the upper left, followed 1 s later by the contextual cue in the upper centre, and followed another 1 s later by a blank comparison square on the upper right. Three comparisons appeared simultaneously in random order across the bottom of the screen. Participants had to drag one of the three comparisons into the blank square using the mouse. When the comparison was dropped onto the blank square, the confirmatory response requirement was initiated: two buttons appeared near the bottom of the screen displaying the captions 'Finish Trial' and 'Start Again,' respectively. Pressing 'Start Again' reset the trial to the start, while pressing the 'Finish Trial' button cleared the screen and produced either the feedback screen (in training) or an ITI (in testing). The feedback screen involved the sample, contextual cue, and selected comparison arranged left to right, along with either 'Correct' or 'Wrong' as appropriate. During the ITI, the screen was cleared for 3 s.
Participants were required to proceed through two fourstage cycles of RCP training and testing. Participants successful in Cycle 1 advanced to Cycle 2 while those successful in Cycle 2 advanced to the remainder of the experiment. Analogous to the training and testing of the Same/Opposite relational network in Experiments 1 and 2, Cycle 1 focused on the target arbitrary relational network while Cycle 2 focused on the control arbitrary relational network.
Cycle 1. During nonarbitrary training (Stage 1), the samples and comparisons were pictures of shapes or objects that differed along a number of different nonarbitrary dimensions (e.g., size). A number of stimulus sets were presented in random order. When participants achieved eight consecutive correct responses they advanced to nonarbitrary relational testing (Stage 2). This was the same as the first stage except that no feedback was provided (i.e., after the response the protocol advanced straight to the ITI) and new stimulus sets were employed. Participants had to achieve 100 % correct responses in the eight trials presented in order to advance; otherwise they were reexposed to Stage 1. During arbitrary relational training and testing (Stages 3 and 4 respectively), the samples and comparisons were the stimuli listed earlier in "Apparatus and Materials." In Stage 3, participants were exposed to the following eight training trials (see Table 2 Training took place in blocks of eight trials, with each trial type presented twice per block. Participants had to pick the correct comparison across eight consecutive trials before they could advance to the next and final stage. In arbitrary relational testing (Stage 4), responses were not reinforced and participants were exposed to the following eight test trials (see Table 2 ]. Participants scoring 22/24 (92 %) were deemed to have passed and advanced to Cycle 2; those failing to reach this criterion were reexposed to all stages of Cycle 1. Cycle 2. Stages 1 and 2 were the same as in Cycle 1. Stages 3 and 4 were identical in format to the same stages in Cycle 1, but differed in terms of the relational networks, with Cycle 2 concentrating on the control rather than the experimental network. Thus, in Stage 3, participants were exposed to the following eight training trials (see Table 2 In Stage 4, participants were exposed to the following eight test trials (see Table 2 to the remaining stages of the experiment. It was intended that those failing to reach this criterion would have been re-exposed to all stages of Cycle 1 but no participant failed the second cycle. Phase (iii) Follow-up function training & testing.
This was identical to initial function training and testing. As explained at the end of Phase (i), correct responding during the testing stage was counted as 100 % responding in accordance with the relational network trained and tested in Phase 2. The following stimuli were samples during the testing stage: A1 (Casors), B2 (Bear), C2 (Vartle), B1 (Lorald), and C1 (Heiter) while the comparisons were the three auditory stimulus buttons that produced either 1, 2, or 3 chimes. In Phase (ii), the target B2 was trained as opposite to A1, a sameness relation was derived between B2 and C2 and opposition relations were derived between B2 and B1 and B2 and C1. Because B2 was trained to have an auditory stimulus function of "1 chime," and, thus, in a context in which the choice was between 1, 2, or 3 chimes, then 3 chimes might be predicted to function as opposite to 1 chime, the following pattern of transformation of functions would be expected: A1 (opposite, 3 chimes); C2 (same, 1 chime); B1 (opposite, 3 chimes); C1 (opposite, 3 chimes). 3 If participants responded 100 % in accordance with this pattern then they advanced to the next phase of the experiment. If not, they were re-exposed to Phase (ii) RCP training and testing. Phases (iv-vi) Suppression induction, cognitive load induction, and suppression task. These were the same as for Experiments 1 and 2.

Experiment 3: Results & Discussion
All ten participants failed Phase (i) Initial function training and testing as predicted. In Phase (ii) RCP training and testing, eight participants passed nonarbitrary training and testing on their first exposure in Cycle 1, while of the remaining two, P9 required one further exposure, while P5 required two further exposures. Six participants required one exposure to Cycle 1 arbitrary training and testing to advance to Cycle 2, while, of the remaining four, P1 and P9 required one further exposure, P3 needed two further exposures and P4 required four further exposures. All ten participants passed all stages of Cycle 2 the 3 One question that might be raised in relation to the pattern of responding shown on the basis of this particular protocol, and which might indeed be raised in regard to the patterns of responding shown on the basis of the nonarbitrary relational training procedures used across all three experiments, concerns the extent to which it might be more accurate to characterise at least some of the responding at issue as comparative than opposite relational responding. In response, even though the training / testing stimuli used in these procedures did indeed vary in terms of size and quantity, and participants were sometimes (i.e., in the presence of the 'opposite' cue), required to choose comparisons that were either bigger / smaller or more / less than the sample, the patterns of responding they showed were always more consistent with opposite than comparison relations at a functional level because on such trials they were always required to choose from amongst several comparisons that were all either more or bigger than the sample or less or smaller than the sample and the correct response always involved choosing the comparison farthest away from the sample in size. The latter is required in a pattern of opposition relational responding but not in a pattern of comparison relational responding and thus any person responding consistently correctly can be considered as showing opposition rather than comparison relations. first time. In Phase (iii) Follow-up function training & testing, all ten participants passed with minimal trials needed.
All participants showed space bar presses (M = 33.1, range=9-105) during the Phase (iv) 5-minute suppression induction phase and, at the end of the experiment, all could at least near correctly reproduce the 9-digit number they were required to memorize in the Phase (v) cognitive load manipulation phase, indicating that they had followed the instructions. Figure 11 shows the mean frequency of removals for seven word categories in the suppression task (analyses suggested no differences between B1 and C1, the stimuli in derived opposite relations with the target and, thus, their data were combined): Data were analysed using a one way repeated measures ANOVA with word category as the 'within subjects' factor. Mauchly's test indicated that the assumption of sphericity had been violated (χ 2 (20) = 37.302, p=.018) and, thus, degrees of freedom were corrected using Greenhouse-Geisser estimates of sphericity (ε=0.524). There was a significant effect of word category, F(3.141, 28.27) = 16.119, p<.001, η p 2 =.642. The results of pairwise comparison t-tests (LSD) are shown in Table 7. Results show the following: that the mean number of responses to the target was significantly different than to all other categories except for the trained opposite word; that the mean number of responses to words in trained opposite and derived same relations was significantly higher than that to all categories other than the target network; that the mean number of responses to words in derived opposite relations was significantly higher than that to words in the non-network and novel categories; and that the mean number of responses to nontarget words was significantly higher than that to the non-network and novel words.

Suppression Task Word Removal Frequency
Overall, these group level results suggest that, as in Experiments 1 and 2, participants were more likely to remove the target and its related words than to remove words from other categories, suggesting transformation of function. Once again though, as for Experiment 2, the pattern is not as strong or as clear cut as for the first experiment, for which there was a clearer distinction between the target network and the nontarget network, for example. Figure 12 shows frequency of removal for each of the seven word categories in the target network (i.e., target, trained opposite, derived same, derived opposite, nontarget network, non-network, and novel) for each individual participant. As may be seen, all participants except one removed the target the maximum number of times. In a number of cases (P1, P2, P3, P4, P5, P6, P10), the trained opposite word was also removed the maximum number of times. The derived members of the target network were removed less frequently but there are still strong trends for them also; for example, the derived same word was removed at least twice by seven participants, while the derived opposite words were removed at least twice by six participants. In addition, as in Experiment 2, there was a general trend whereby participants removed words in the target network more often than they removed words in other categories, indicating transformation of function. However, as suggested above, the pattern of acquisition of functions for members of the nontarget relational network seems relatively stronger in this experiment than in Experiment 1. For example, there were three participants (P4, P5, P7) who appeared to show relatively strong acquisition of functions for the nontarget relational network. Data were analysed using a one way repeated measures ANOVA with word category as the 'within subjects' factor. Mauchly's test indicated that the assumption of sphericity had been violated (χ 2 (20) = 43.929, p=.003) and, thus, degrees of freedom were corrected using Greenhouse-Geisser estimates of sphericity (ε=0.480). There was a significant effect of word category, F(2.88, 25.916) = 18.656, p<.001, η p 2 =.675. The results of pairwise comparison t-tests (LSD) are shown in Table 8. The pattern for removal latency was similar to that for frequency though not identical. The mean latency to the trained opposite word was significantly lower than that to all categories other than those categories within the target network. The mean latency to the words in derived same and derived opposite relations was significantly lower than that to words in the non-network and novel categories. And the mean latency to words in nontarget and non-network categories was significantly lower than that to novel words.
These group level results suggest that, as in the previous experiments, participants were faster to remove the target and words related to it than to remove words from other categories, suggesting transformation of function. Once again, though, the pattern is less clear than for Experiment 1, with less difference between the target and nontarget networks. Figure 14 shows the latency of removal for each of the seven word categories in the target network (i.e., target, trained opposite, derived same, derived opposite, nontarget network, non-network, and novel) for each individual participant. The target was typically removed faster than any other category of word. In addition, in the case of seven participants (P1, P2, P3, P5, P6, P7, P10), either all or all but one of the words in the target network were removed faster than words in other categories. However, in the case of a number of participants, words in the nontarget network were removed relatively fast also.

Summary and Discussion of Findings for Experiment 3
Experiment 3 aimed to extend the results of Experiments 1 and 2 by showing a conventional pattern of transformation of functions though opposition relations alongside the samenessconsistent transformation of thought suppression functions via nominally opposite relations shown in the previous two experiments. To do this, ten novel participants were recruited and were first trained and tested for discriminative functions (of selecting along an auditory nonarbitrary dimension) in several textual stimuli including the word 'Bear'. They were then trained and tested for arbitrarily applicable relational responding in accordance with 'Same' and 'Opposite' using the 'Relational Completion Procedure' before being reexposed to the test for discriminative functions. All ten participants showed predicted patterns of transformation of functions consistent with 'Same' and 'Opposite,' respectively. They were then exposed to the same thought suppression protocol as previous participants had received and, in the final stage of the latter, showed a similar sameness-consistent pattern of transformation of functions as shown by the earlier participants and, in particular, those in Experiment 2 for whom the same-opposite relational network established was identical. Experiment 3, thus, contributes to this overall study in two respects. First, it replicates the pattern of transformation of functions via derived same and opposition relations seen in the first two experiments and, in particular, that seen in Experiment 2. Second, it juxtaposes the demonstration of samenessconsistent transformation of functions via both nominally same and nominally opposite relations with the demonstration of patterns of transformation of function defining of same and opposite, respectively, thus, providing more definitive evidence that the relational pattern seen throughout all three experiments did indeed involve opposition relational responding in at least some contexts and, hence, that in the context of derived thought suppression, relations established as nominally opposite can function as sameness relations.

General Discussion
Previous research demonstrated transformation of thought suppression functions based on derived equivalence relations (Hooper et al. 2010). In so doing, it extended work by Wegner et al. (1991Wegner et al. ( , 1992 by empirically modelling a process of indirect thought suppression interference. However, from a 'Relational Frame Theory' perspective, equivalence or sameness relations are only one type of derived relation and other types may be even more relevant than equivalence as regards indirect acquisition of thought suppression functions in particular. For example, it might be supposed that someone trying to suppress a thought would think of something that is opposite to the suppression target along one or more important  dimensions. For instance, someone trying to suppress a depressing thought might think of something happy or joyful, while someone trying to suppress an anxiety-provoking thought might imagine something safe or relaxing. Hence, given the potential importance of the relation of opposition in this regard, the current study examined transformation of thought suppression functions via trained and derived opposition relations. In each of the three experiments in the current study, participants were trained and tested for formation of two five-member relational networks composed of nominally 'same' and 'opposite' relations. They were subsequently instructed to suppress a target word, which had previously appeared in one of the two relational networks, while a number of words appeared on the screen in front of them in a quasi-random cycle, including the target, words nominally participating in a target relational network, words participating in a nontarget relational network, and other control words. As in Hooper et al. (2010), participants were allowed to remove any word that appeared on the screen by pressing the computer spacebar.
Overall, across experiments, there was some indication that target words were removed more frequently and more quickly during the suppression task than other words trained to be members of the same relational network. However, in contrast to the same and opposite relations nominally trained within the target network, there were no differences in frequency or latency of removal across stimuli, regardless of training relations (and regardless of direct or indirect conditioning). Furthermore, stimuli assigned to the target relational network were generally responded to more frequently and more quickly during the suppression task than were control stimuli. This pattern of responding indicates that the relational training procedure interacted with a participant's pre-experimental learning histories to frame all of the stimuli in the target network with sameness, as evidenced by the equivalent transfer of suppression functions to all stimuli participating in that network during the suppression task.
One arguable limitation of Experiment 1 was that there was only one identified relation of opposition in the target network and it did not allow a very comprehensive investigation of transformation of function via opposite relations. The purpose of Experiment 2 was to allow for a more thorough investigation of change of thought suppression functions via relations of opposition. In this experiment, the target word was trained as 'opposite' to the hub word in the relational network and thus (a) all the ensuing derived relations and changes of function were based on a trained relation of nominal opposition, and (b) the network primarily involved relations of opposition rather than relations of sameness. Experiment 2 extended the results of Experiment 1 by demonstrating a sameness-consistent transformation of thought suppression functions via trained relations of nominal opposition as well as via a derived sameness relation that was itself based on two nominally opposite relations.
One of the criticisms of both Experiments 1 and 2 was that, because they only showed a sameness-consistent transformation of functions via nominal or purported relations of opposition, then perhaps the relations demonstrated were not opposition relations. The aim of Experiment 3 was to investigate the possibility of showing a conventional transformation of functions though opposite relations alongside the samenessconsistent transformation of thought suppression functions through these same relations, thus demonstrating that the latter functioned as relations of opposition in at least some contexts. To this end, ten novel participants were first trained and tested for discriminative functions in several textual stimuli including the word 'Bear.' They were then trained and tested for arbitrarily applicable relational responding in accordance with 'same' and 'opposite' using the 'Relational Completion Procedure' before being re-exposed to the test for discriminative functions. All ten participants showed sameness-and opposition-consistent transformations of functions of stimuli participating in 'same' or 'opposite' relations respectively with 'Bear.' They were then exposed to the same thought suppression protocol as previous participants had received and showed a similar pattern of sameness-consistent transformation of functions throughout the relational network as shown in Experiment 2, during which the target stimulus was trained to be in opposition with the hub stimulus (A1). Experiment 3 thus replicated the pattern of transformation of functions through derived same and opposition relations seen in the first two experiments and, in particular, the pattern seen in Experiment 2, and constituted evidence that in the context of derived thought suppression, stimulus relations that are functionally opposition relations in other contexts can be functionally sameness relations.
As regards procedural variations across the current study, one point that might be made is that, because what people might try to do is think of something in a direct relation of opposition from the to-be-suppressed stimulus, then it would seem that the second and third experiments in the current study, both of which involved a trained relation of opposition between the target and the remainder of the network, would be a closer model of 'real life' thought suppression via opposition relations than Experiment 1. However, this suggestion might itself be further empirically explored in future research using the current paradigm by, for example, requiring people to suppress particular real world concepts through distraction and examining the actual relational networks involved.
This research did not simply examine results at a group level but also examined findings at the individual level. Adding to the relative clarity of the group-level results, in each of the experiments, there were clear cut examples of the transformation of functions via same and opposite relations, both trained and derived, at the individual level also. Naturally, however, there was also variability in performance such that, in the case of some individuals, the predicted pattern of transformation of functions was not seen. Such individual variability certainly warrants further investigation. It is possible that, in the case of some participants, there was a lack of attention to the instructions or a lack of rule following. During an experimental cycle, participants were required to pay close attention to the computer screen for a period of almost twenty minutes during the suppression task, which followed a lengthy procedure of training and testing arbitrary relations. Thus, it is perhaps not surprising that there might have been variable attention and or adherence to instructions. To investigate this further and isolate the processes of interest more effectively, it would be advisable for future research using this type of protocol to use adherence measures.
As stated in the introduction, the current study used a procedure for training and testing relations of sameness and opposition relations similar to that employed by Whelan et al. (2005). The latter researchers demonstrated priming effects based on derived relations of sameness and opposition whereby participants responded more quickly to pairs of arbitrary stimuli if they were in either directly trained or derived relations of either sameness or opposition than if unrelated. This phenomenon of priming is also directly relevant to the current paradigm since thought suppression interference can also be conceptualised as a type of priming, albeit with different response outcomes. As such, the results of Whelan et al. (2005) might even have been used to predict the current outcome.
These results provide further empirical evidence of the difficulty of thought suppression. This is related to a number of additional points. One point previously made in the introduction pertains to the fact that the phenomenon of "thought suppression" studied here may be more like distraction than pure suppression as conceptualised by Wegner (e.g., 1989). Future research could perhaps use the paradigm employed here as a basis for further exploration of this distinction and to compare these two phenomena. This is related to a second point that could be made regarding the investigation of thought suppression in the current study. While objective measures of thought suppression were enabled through recording of space bar pressing, additional information concerning the processes at work might have been provided by using 'talk aloud' procedures to have participants report on the strategies they employed in order to avoid thinking about the target during the suppression phase. Such reports might have provided information on the frequency of use of suppression versus distraction strategies both within as well as across participants. It might have provided more detailed information concerning the extent to which particular stimuli acted as useful distractors as opposed to causing the failure of thought suppression. Such information might help explain response patterns seen in the findings of the current study. For example, there appeared to be low, but nonetheless detectable, responding towards stimuli that did not participate in the relational networks. Perhaps aspects of Wegner's basic ECH theory or other theoretical conceptualizations might help explain these effects. Clues might be provided by soliciting verbal descriptions from participants. As such, this is therefore a recommendation for future work with this paradigm.
As has been suggested, these findings provide further empirical evidence of the futility of thought suppression. They also provide further evidence of the contention by many thirdwave approaches to psychotherapy, including "Acceptance Commitment Therapy" (ACT; Hayes et al. 1999;Hayes 2004), for example, that stress the importance of acceptance rather than control as an approach to unwanted thoughts. RFT provides a technical explanation for why this is the case. From an RFT perspective, responding relationally always involves at least two key forms of contextual control. One is control over the derivation of the relations itself, which is referred to as C rel control. For example, in the statement 'A is the same as B,' a key cue for the relation to be derived is the word 'same.' The second form of contextual control concerns which functions are transformed via this relation. This is referred to as C func control. For example, in a context in which A is a thought that a person is trying to avoid, then because B has been derived as being the same as A then B may acquire similar functions such that a person will want to avoid B also. On the other hand, in a context in which a person can accept the thought A then he/she can also accept the thought B. Traditional second-wave approaches to psychotherapy have been characterised by their emphasis on what RFT would interpret as C rel interventions, in which the therapeutic process is seen as an attempt to change the relations that are derived. For example, if a client suggests that he or she has thoughts that 'I am bad' (the C rel here is 'am'), then the therapist might try to provide the client with sufficient evidence to convince him or her to think 'I am not bad' or 'I am the opposite of bad' (C rel = 'not' or 'opposite'), a better representation or a 'truer' thought. However, as empirical data such as that provided by the current study suggest, this may ultimately be ineffective because in the context of thought suppression, the relation being derived (i.e., whether 'same' or 'opposite,' for instance) does not matter and, ultimately, the same problematic avoidance responses that are performed with respect to 'I am bad' will be performed with respect to 'I am not bad.' Rather than C rel interventions, third-wave approaches such as ACT tend to instead recommend C func interventions. In this approach the client is encouraged to change the context for thoughts such as 'I am bad' rather than to change the relation derived. For example, he or she might be encouraged to respond to particular thoughts with acceptance rather than suppression or avoidance. From this perspective, this change in the functional context (C func ) for such thoughts is ultimately more likely to be successful than changes to the relational (C rel ) context because in the long run, the client has more control over processes characterising the former than those characterising the latter.
In conclusion, the current studies have extended previous work by Hooper et al. (2010) who demonstrated derived thought suppression interference via equivalence by providing empirical evidence that this effect occurs not just via coordinate relations but also via non-coordinate relations and, more specifically, opposition relations. Future research exploring issues and implications of these findings for understanding thought suppression and other forms of cognitive control will be important for both basic and applied purposes.