A Working Memory System With Distributed Executive Control

Task-control processes

Several kinds of processes are involved in this competition. To clarify these processes, let us take as an example switching from the execution of a magnitude judgment task (deciding whether a digit is smaller than or larger than 5) to a parity judgment task (deciding whether a digit is odd or even). The parity task requires the categorization of a digit as odd or even; in the magnitude task, the same digit must be categorized as small (smaller than 5) or large. In other words, the correct response to the digit depends on the task. In this particular case, one of two keys must be pressed. For the parity task, the instruction is to respond with a left key press when the digit is odd and with a right key press when it is even. Similarly, the magnitude task requires a left response for a small digit and a right key press for a large digit. Each trial starts with a cue that indicates which task must be performed. The cue is followed by the presentation of a digit.

Using this pair of tasks, Figure 1 illustrates how the execution of the parity judgment task may be affected by previous executions of a magnitude judgment task. The figure shows four pathways that are involved in the competition between goal-directed (Pathway 1) and interference-based (Pathways 3–4) processing. The cue initiates goal-directed processing. Via a learned association, the cue points to a task goal that after activation results in the configuration of the task set (Pathway 1), which is an ensemble of task-execution parameters (Logan & Gordon, 2001). For the tasks in the example, the task set includes settings of the orientation of attention (attention focused on a point in space where the digit will appear), stimulus categorization rules (categories odd and even for the parity task; small and large for the magnitude task), response mappings (e.g., press left key for odd), stimulus modality (visual or aural presentation of digits), response modality (manual or vocal response), and speed-accuracy trade-off (stress on accuracy, stress on speed, or equal stress on both).

OPEN IN VIEWER

Fig. 1.

Schematic description of the stages involved in goal-directed processing. In the top-down pathway (1), first a goal is selected (parity: odd/even judgment). This leads to configuration of the corresponding task set and biasing of the stimulus categorization towards the odd-even judgment rules. In the bottom-up pathway (2), the stimulus is linked with both the magnitude (small/large) and the parity categorization (in bold). Due to top-down biasing, the correct stimulus categorization is selected, which leads to a correct response. In previous episodes, a stimulus-response association (3) may have been learned; this association automatically triggers the previously associated response. If this response is incorrect, the conflict between the incorrect and the correct responses must be resolved. It is also possible that in previous episodes, a stimulus-task association has been formed, for example, with the magnitude task (4). This leads to a goal conflict, which propagates all the way down via task set and stimulus categorization to response.

Activation of the goal and configuration of the task set take some time, after which the conditions are set for activation of processes that result in goal achievement (Logan, 2003; Meiran, 1996, 2000; Monsell & Mizon, 2006; Rogers & Monsell, 1995). These processes include activation of the target categorization (e.g., odd), activation of the category-response mapping (if odd, press left), and finally activation of the motor response (left key press). Some of these processes are so well practiced that they also occur via direct target associations (Pathway 2). Such direct association may activate an irrelevant categorization, which in turn may activate its associated response, thus creating a competition with the task-relevant chain of events.

Repetitions of stimuli or stimulus features prime repetition of the associated response (Pashler & Baylis, 1991a, 1991b). The direct stimulus-response (S-R) association (Pathway 3) can bypass the goal-directed pathway (1) to the response. Task repetition enhances performance efficiency, but when the task changes, application of the S-R association may result in an error. Controlled processing is needed for the goal-directed processing pathway to be favored over the direct S-R link (Schuch & Koch, 2003; Verbruggen, Liefooghe, & Vandierendonck, 2006).

Research has also shown that the target stimulus can become associated with the task (Waszak, Hommel, & Allport, 2003), resulting in the creation of a stimulus-task association (Pathway 4). When a particular target is uniquely linked to one of the tasks (e.g., when the digit 2 would only occur in the context of the parity task), a direct stimulus-task association (2-parity) bypasses effortful goal-directed processing and results in faster goal achievement without risk of errors. However, when occasionally the target occurs in the context of the other task (e.g., the digit 2 unexpectedly occurs in the context of the magnitude task), goal achievement of the magnitude task may completely fail. The occurrence of such a bypass is difficult to control because the stimulus-task association directly activates the task goal. If this activation is fast, the incorrect task goal may be the first one becoming active so that it can easily win the competition from the correct goal. If on the contrary, activation of the correct goal occurs first, it is more likely to win the competition.

This brief sketch summarizes the task-processing stages at which biases and processing conflicts may occur. At each of these stages, cognitive control operations resolve the conflicts to achieve the relevant task goal. More detailed information can be found in the literature on task-switching and dual-tasking performance (J. W. Brown, Reynolds, & Braver, 2007; Gilbert & Shallice, 2002; Kiesel et al., 2010; Logan & Gordon, 2001; Monsell, 2003; Vandierendonck et al., 2010; Waszak et al., 2003).

Interaction with WM

Notwithstanding the huge number of articles published on task switching in the last two decades, the number of studies of the relationship between task switching and WM is rather modest (Kiesel et al., 2010; Vandierendonck et al., 2010) and addresses only three research questions, namely, the role of verbalization in task switching, the trade-off of WM and task-switching efficiency, and the role of WM in voluntary task choice. Because of their relevance to the present concern (i.e., how task-switching processes constrain the WM architecture), I consider each of these three lines of research in some detail.

Procedural knowledge base

The procedural knowledge base consists of condition-action rules. These rules can be quite simple, such as “IF number is even, THEN press right button” or “IF a plus cue is present, THEN instantiate ‘addition of 1’ as the goal,” but they can have rather complex condition parts such as “IF the goal is parity judgment AND the number is 3, THEN categorize the number as odd,” or “IF a plus cue is present AND the goal is subtraction, THEN suppress the subtraction goal,” or even “IF a goal is addition and a goal is subtraction, THEN set the goal-conflict flag.” These examples show that when applied, some of these rules initiate a motor action (e.g., “press right button”); others update WM contents either directly (e.g. “suppress subtraction goal”) or after performance of a cognitive action (e.g., “categorize as odd”); still others may simply change a parameter setting in the task set (e.g., “set goal-conflict flag”).

The rules in these examples have all been acquired. Although some procedural knowledge is innate (e.g., “IF pain is felt, THEN cry,” or “IF feeling hungry, THEN eat”), most of this knowledge is acquired from experience and practice, but rules can also be acquired by instruction (Cohen-Kdoshay & Meiran, 2007). Procedural learning occurs in a number of ways: by adapting the rule strength of existing rules, creating completely new rules, or combining existing rules. Each production rule has a strength or confidence value that changes on the basis of experience: the more often a rule has been successfully applied, the more the confidence in the rule has accumulated; similarly, after unsuccessful application, the confidence decreases. Creation of a new production rule occurs if the current WM content is taken as the condition and the produced output is taken as the action. For example, when the answer “5” in response to the attended stimulus “2 + 3 = ?” is rewarded, the rule “IF goal is to add two numbers AND the sum of 2 and 3 is requested, THEN say 5” may be created. Initially, this rule will have a rather low confidence value, so that the likelihood of its being activated is rather low. However, when one must solve the same problem again, the rule may be recreated, leading to an increased rule strength. After a sufficient number of successful rule applications, the rule may have gained so much strength that it always gains the competition. As discussed previously, it is well known that during execution of simple cognitive tasks, new S-R rules (in line with Pashler & Baylis, 1991a, 1991b) and new stimulus-task rules (in line with Waszak et al., 2003, 2004, 2005) are created. Apart from these two elementary forms of rule learning, a new rule also can be created by combining existing ones. If two rules with the same action part have conditions that differ, a new rule encompassing both conditions may be created, which results in a more general rule. This possibility is important in categorization; use of the rules “IF there is a square AND its color is red, THEN say Category A,” and “IF there is a square AND its color is blue, THEN say Category A” forms the more general “IF there is a square AND it has any color, THEN say Category A” (e.g., Anderson, Kline, & Beasley, 1979). Other possible rule combinations may result in rule specialization or even in the creation of chained rules.

Processing engine

The procedural knowledge base in LTM can thus be characterized as a repository of procedural rules. A processing engine handles the activation and selection of the relevant rules. Only when the condition part of a rule matches one or more WM contents, the rule can be applied. The rules that match WM contents are flagged as applicable, and from this applicable set, only the most relevant rules are allowed to fire, which means that their action part is executed.

How can it be determined that one rule is more relevant than another one? Assessment of relevance may depend on several features. Rule strength is a first possible feature. A rule with a high strength or confidence value has proven to be successful and therefore may be considered to be more relevant than rules that have accumulated less strength. However, even when a rule has built up strength in a particular context, it may be less relevant for the present context than a weaker rule. For example, the more general rule “IF it is cloudy, THEN it will rain” may be stronger than the rule “IF it is cloudy and it is freezing, THEN it will snow”; however, if both match, the latter rule would be more relevant because it applies to more specific conditions. For that reason, rule specificity also should be taken into account on the assumption that a more specific rule is more likely to be useful in the present context than a more general rule (see also Holyoak, Koh, & Nisbett, 1989). This point can be clarified by comparing a few examples: “IF category is even, THEN press right button”; “IF goal is parity AND category is even, THEN press right button”; “IF goal is parity AND number is 4 AND category is even, THEN press right button”; and “IF binding contains parity goal AND number 4 AND category even is present, THEN press right button.” These examples have all the same action part, but they differ in the generality of the conditions so as to form a hierarchy. The fewer elements that are specified in the condition, the more general the condition is; conversely, the more elements the condition contains, the more specific it is. The last rule in this list of examples is very specific in that it specifies the current goal, the digit, its categorization, and the existence of a binding of these elements. If all these components are present in WM, then it is quite likely that this rule is relevant to the presently existing context. In contrast, the first example in the series only mentions the category “even.” Although the rule has some relevance, it is far less specific because it also would match when another goal is present and the category representation in WM is a leftover from a previous event.

A further feature that can be used to assess relevancy is the degree of match. In many production systems (e.g., Anderson et al., 1979), matching is either all or none, but it is perfectly possible to consider matching as a matter of degree (e.g., Vandierendonck, 1995); a higher degree of matching corresponds to a higher degree of relevance of the rule. In sum, the rules selected to be most relevant will be the ones with the highest confidence value, the highest degree of match to the existing conditions, and the most specific conditions for the same proposed action.

Checking of WM contents for applicable procedural rules occurs according to a scheduled process. To that end, the processing engine performs a continuously cycling processing loop consisting of a series of actions, including processing of environmental inputs, checking for conflicts, adapting WM contents, and initiating motor actions. In every cycle, some procedural rules that match WM contents are applied. Each rule application takes some time, so that the next cycle of checking can only start after rule application has finished. It is also important to note that not every rule applied contributes to achieving the intended goal. For example, some rules provide a shortcut between stimulus and response, actually bypassing the task set specifications. When other processes do not block the bypassing action, an action slip (error) is bound to occur.

Task switching

In many studies of task switching, researchers have investigated switching between numerical judgment tasks, such as parity and magnitude judgment (e.g., Logan & Bundesen, 2003). These tasks were included in examples presented earlier in this article. To illustrate how control processes are conceptualized in the present model, I have used these tasks again. In the present case, each trial starts with the presentation of a digit shown either in blue (signaling the magnitude task) or in red (calling for the parity task). The parity judgment task requires a left key press for an odd number and a right key press for an even number; the magnitude judgment task requires a left key press if the number is smaller than 5 and a right key press if the number is larger than 5; the digits are centered on a screen; responses are expected to be fast but correct. All this information is presented in the instructions and is stored in LTM. Notwithstanding evidence suggesting that an immediate procedural encoding occurs (Cohen-Kdoshay & Meiran, 2007; Liefooghe, De Houwer, & Wenke, 2013), some practice is included to stabilize the procedural encoding of all this information.

Each trial of the experiment starts with the appearance of a digit in the center of the screen—say, for example, a red digit 3 on the current trial. As the appearance of the digit involves a change in the visual environment, it (automatically) captures attention. This capture leads to its instantiation in WM, presumably in the episodic buffer but possibly also in the phonological loop. ⁵ The color feature of the digit matches the rule that translates the color into a goal (“IF color is red, THEN select parity goal”), which results in the instantiation of the goal name in the episodic buffer. Next, the task set is retrieved from procedural LTM and configured in the executive module. The present example includes two category-response rules (“IF odd, THEN press left,” and “IF even, THEN press right”), a parameter setting that a manual motor response is required, and a parameter setting that both speed and accuracy are required. Thus far, the WM contents match rules regarding parity goals, parity task sets, and digits. The combination of goal and digit matches some rules, for example, a rule such as “IF goal is parity and digit is 3, THEN retrieve category odd.” If this rule is applied, the digit parity (odd) will be added to the episodic buffer. On a next processing cycle, the presence of the goal, the digit (target), and the category may trigger a rule to create a binding of these elements in the episodic buffer. This binding may then trigger a rule to activate the corresponding response rule that is part of the task set. After sufficient activation has been accumulated, a left key press response will be executed. This sequence of processes corresponds to Pathway 1 of Figure 1, and involves both the episodic buffer and the executive memory module.

With more practice in the task, the LTM rule linking the digit and the parity category becomes stronger and may be triggered automatically, resulting in simultaneous instantiation of the digit and its parity category in the episodic buffer (Pathway 2 in Fig. 1). Thus, the time needed to complete processing of the target is shortened, with as a consequence faster correct responding.

When the category “odd” is instantiated in the episodic buffer, irrespective of whether this occurs due to activation of the shortcut just mentioned or whether the category is retrieved on the basis of the combination of digit and goal, an error may occasionally occur. For example, when the present digit (3) and the category “odd” are in the episodic buffer while the previous category (“even”) is still present, both the triplet “parity goal, 3, odd” and the triplet “parity goal, 3, even” meet the conditions of a rule to form a binding. Only one of those bindings can be implemented because each particular element can be present in only one binding at any time. Whichever of the two bindings is implemented first will constrain further response selection. In other words, if the parity-3-even binding is implemented first, the even-right rule in EM will be triggered, even though the present digit is odd.” This example shows that the processes involved in binding the WM elements are “blind” to the precise features of their inputs and hence do not “know” which binding is the correct one.

In contrast to repeat trials (trials in which the task or goal remains the same), switch trials require retrieval and configuration of a different task set, which makes performance vulnerable to sources of interference such as target-response associations and target-task associations. In typical task-switching contexts, all the targets are randomly distributed over the tasks, so that each digit occurs about equally frequently in each task. Thus, if an association between a particular digit and a specific task is formed, the association between the same digit and the other task are roughly equally strong, so that there is no real danger of such an association bypassing processing. Similarly, if an association between a particular digit and a correct response under a particular task is formed, the association between this digit and the alternative response has a similar strength. The likelihood that such an association bypasses processing is also rather small.

Nevertheless, it is worthwhile to explore what would happen if such associations could acquire enough strength to affect performance. First, I examine the case of a target-response association (Pathway 3 in Fig. 1). Consider the case that over a series of magnitude judgment trials, an association between the digit 7 and the response right (IF digit 7, THEN respond right) has built up strength and that the present trial shows the digit 7 in a parity task. If the association has sufficient strength, the right key press may be gaining strength while instantiation of the parity goal and the corresponding task-set reconfiguration still have to be completed (as in Pathway 1 of Fig. 1). If the strength of the respond-right process reaches threshold before target-related processing is complete, an incorrect and, in fact, unintended response will be made. The only way to safeguard against such fast errors is to make it more difficult for the unintended response to be made by raising the response-threshold setting (in EM) so that responding overall becomes slower. ⁶ This extra time before responding completes allows goal-directed processing to configure the task set and to build up strength in favor of the correct response. The result is that on some occasions the incorrect response will be executed while on other occasions the correct response will be produced.

Next is the case of target-task associations (Pathway 4 of Fig. 1). This case is based on the acquisition of an association between the target digit and the task name (“IF digit 7, THEN instantiate magnitude goal”) within the context of the same example of the digit 7 occurring only in the magnitude task over a series of trials. When the digit 7 occurs while the magnitude task set is already configured, application of the rule only strengthens the present goal and task-set representations. However, if the digit 7 is presented for parity judgment (as indicated by its color), two incompatible goals may become instantiated in the episodic buffer: the parity goal (on the basis of the color cue) and the magnitude goal (on the basis of the acquired association). These instantiations will be accompanied by instantiation of the corresponding task sets in EM. The presence of incompatible goals in the episodic buffer or incompatible task sets in EM constitutes a goal conflict. If a conflict-detection rule fires in response to the goal conflict, a goal-conflict flag is set because further processing of two incompatible intentions is bound to result in incoherent responding. As a safeguard, when the goal-conflict flag is on, only goal- and task-set-relevant rules are allowed to fire. When the conflict is resolved, the conflict flag will be turned off. In the meantime, only goal instantiation, goal inhibition, and task-set-configuration rules are allowed to fire, with the result that one of the two goals wins the competition. Because goal and task-set instantiations of both tasks start at about the same time, either of the two may win the competition, resulting in either a slow correct or a slow incorrect response.

This account of the rule applications in a task-switching context shows that there is no need for a special agent to control the events and actions. Instead, in the four processing pathways that have been well documented by previous task-switching research, the actions performed are completely accounted for by the contents of the WM modules and the rules available in procedural LTM. Because the rules vary in strength, the time course of WM instantiations shows some variation, resulting also in variable responses and response times. So, even though the interaction of conditions and rules follows fixed principles, the resulting behavior of the system still is variable.

Intentional memorization

Although memorization without explicit intention to retain the information for later usage does occur, in the context of WM research with its focus on serial recall, storage is driven by an intention to use the stored information. Because of this intentional basis, this activity is assumed to involve, like any other intentional activity, a representation of the memorization goal and a corresponding task set. Given that the task set specifies the means to attain the goal, it seems evident that the task set encoded in EM would include one or more of the “strategies” that could be used to efficiently store and maintain information in memory, such as encoding, chunking, grouping, rehearsing, or refreshing. To cope with anticipated requirements of recall (e.g., a focus on item information, particular item features such as location or color, or the serial order of items), one selects a suitable memorization method, and it is encoded in the task set. Other task constraints such as expected modalities of recall also are part of the configured task set.

The presence of a memorization intention thus affects the maintenance operations performed during a retention interval. In a typical WM task, serial position of the memoranda is important, so rehearsal and refreshment have to respect order coding. Similarly, if chunking is used, the chunks have to respect the order of the individual memoranda.

Once the memorization goal and task set are prepared, each occurrence of a new memorandum has to be stored in WM in accordance with the memorization rule and parameters specified in the task set. In the interval between successive memoranda and during the retention interval at the end of the list of memoranda, some operations are performed to enhance the likelihood of later retrieval of the memoranda. These operations are specified in procedural LTM and result in different actions depending on the modality of the memoranda. For memoranda stored in the phonological loop, regular rehearsals are performed, whereas for memoranda in the episodic buffer, refreshments are more likely to be used (for more details about this difference, see Camos, Lagner, & Barrouillet, 2009; Camos, Mora, & Barrouillet, 2013; Camos, Mora, & Oberauer, 2011; Mora & Camos, 2013).

When recall is requested, the memorization goal is replaced by a recall goal and corresponding task set. This task set specifies the output modality required for recall (oral recitation, written recall, old/new decision, and so on). A recall loop is started, such that in each cycle of the loop, the WM contents are scanned, and the memoranda recovered are encoded in the output buffer and eventually emitted.

Dual-task: Task execution during retention interval

The model’s account of the control processes occurring in a dual-task context involves both memorization and task execution. In the case considered here, a series of tasks must be performed during the retention interval of a memorization task. Many dual-task studies have reported an impairment of serial recall when a secondary task is performed during the encoding interval, the retention interval, or both. Controlling for time available for memory maintenance and secondary task execution, the methodology introduced by Barrouillet et al. (2004) has become a standard in the field to test TBRS theory. A simple experiment reported in Barrouillet, Portrat, Vergauwe, Diependaele, and Camos (2011) is used here to illustrate how the model accounts for control processes in such a dual-task setting.

In this experiment, memoranda were seven consonants, each followed by an interval during which either four or eight squares were presented at a slow (1,190 ms per square), medium (990 ms per square), or fast pace (790 ms per square). The participants judged whether the location of the square was above or below the screen center. In the theory tested in this experiment, memory refreshment and task execution are assumed to require attention, which is a resource that can be shared in an all-or-none manner among different tasks. Hence, during the retention interval, attention allocation rapidly switches between the location decision tasks and memory refreshment. That means that while attention is occupied by the location decision task, attention is not available for memory refreshment: The larger the proportion of the retention interval that is occupied by decision tasks, the smaller the proportion of time that will be left for memory refreshment, and the more recall will be impaired. As expected on the basis of the theory, recall was poorer with faster presentation rates, but the number of squares in the interval did not affect recall performance because the cognitive load (proportion of the interval occupied by the decision tasks) did not change.

How does the present model account for such findings? At the start of each trial, the memorization goal is instantiated in the episodic buffer, and the memorization task set is configured in EM. Next, the first memorandum is presented and encoded in the episodic buffer. Soon after encoding and refreshment have started, the first square is presented. As appearance of the square constitutes an environmental change, attention is captured, resulting in the instantiation of the location-judgment goal in the episodic buffer and configuration of the corresponding task set in EM. With this shift from memorization to location judgment, the memorization task set must be inhibited. However, the amount of inhibition applied to the memorization task set can be assumed to be limited because the memorization rules and the location-judgment rules respond to different conditions, so that there is little opportunity for overlaps between application of the memorization and the location-judgment task sets. As a consequence, the chances for mutual interference are rather small, and it suffices to ensure that the location-judgment task set is more strongly activated than the memorization task set. Furthermore, execution of the memorization task has to continue afterwards, so that it is more advantageous to keep the memorization task set in WM so that it can be swiftly reactivated when the opportunity arises. In fact, the context of the retention interval may be considered as one in which the memorization task is interrupted in favor of execution of another task.

When the location-judgment task set becomes the dominant one (i.e., is more activated than the memorization task set), the location of the square must be judged. The features of the square (form and location) become encoded in the visuospatial sketch pad, procedural rules to determine the location with respect to the reference become active, and the result of the process is a categorization response (“above” or “below”) that is instantiated in the episodic buffer, where it can be bound with the goal and the target to activate the appropriate task-set rule (e.g., “IF a square is above center, THEN press left key”). After response execution, application of a rule matching the condition that a response has been emitted reactivates the memorization goal and task set and suppresses the no-longer-relevant location-judgment goal and task set so as to make the memorization task set dominant. The memoranda are now further refreshed until the next square is presented, which leads to a switching back to the location-judgment task. The remainder of the trial entirely consists of such switching back and forth between the memorization and the square-judgment task, and this switching continues until the next memorandum is presented or recall is requested. This state of affairs involving task-set switches ensures that the two tasks are performed strictly sequentially: No memory refreshments occur during location judgment, and no square processing occurs during memory refreshment. Without any need for additional assumptions, it follows that if more of the interval is occupied by location judgment, less time will be available for memory refreshment and that consequently more memory loss may occur. Clearly, this account makes the same prediction as Barrouillet’s TBRS theory. Moreover, this prediction can be made without any call on a central executive or an attentional resource.

Interim conclusion

Clearly, for the all situations considered here, goal achievement is possible without an autonomous agent such as a central executive. In all the examples, the conditions represented in WM are sufficient to trigger specific condition-action rules that either change WM contents or initiate a response that achieves the goal. Occasionally, shortcut rules may be applied that sometimes result in the selection of an incorrect action or lead to a conflict that must be resolved and again may result in an error. In fact, the presence of such rules provides a more straightforward explanation of the occurrence of errors than a central executive that fails on some occasions.

Backward counting

Backward counting by 3 as in the early studies of decay in short-term memory (J. A. Brown, 1958; Peterson & Peterson, 1959) is one of the first tasks ever used to interfere with memory refreshment. Backward counting requires the repetitive application of a “minus 3” operation. This task can be performed by implementing the appropriate task set: subtracting 3 from the target number and then replacing the target number with the result of the subtraction. Application of condition-action rules in response to current WM contents suffices to perform this task repetitively.

Random generation of elements from a set

Another often-used task consists of random generation of elements from a set. For example, imagine repetitively throwing a die and announcing the upcoming number. Such tasks have been performed with letters or numbers (Baddeley, 1966; Robbins et al., 1996; Towse & Cheshire, 2007; Towse & Valentine, 1997), with selection of keys on a key pad (Baddeley, Emslie, Kolodny, & Duncan, 1998), and with time intervals (Vandierendonck, De Vooght, & Van der Goten, 1998a). All these variations of random generation involve simple control processes that mostly are triggered by instructions not to repeat the same item too often or not to produce familiar patterns or orders. Consequently, the task set specifies not only the requirement to retrieve elements or maybe strings of elements (Vandierendonck et al., 2012) but also the constraints that have been stressed in the instructions. All processes needed for executing such a task rely again on condition-action rules that are applied when they match the WM contents. The additional constraints stored with the task set activate rules that check for the presence of repetitions or familiarities. ⁷

In random-interval repetition (Vandierendonck, De Vooght, & Van der Goten, 1998b), auditory stimuli (bleeps) are presented at random time intervals, and each detected bleep requires a fast detection response. The random variation of the time intervals discourages automatization of the detection response and again condition-action rules suffice to correctly execute the task.

Choice response

Most frequently, choice response tasks (Szmalec, Vandierendonck, & Kemps, 2005) are used in dual-task studies. Such tasks (e.g., parity judgment, location judgment, and so on) require selection of an appropriate response. Also the trails task (Lezak, 1983) has been used in some studies (Baddeley et al., 2001). The most difficult version of the task requires alternating between two well-known series (e.g., alternate between reciting days of the week and months of the year: Wednesday, March; Thursday, April; and so forth). Even though each series is well known, progress in each series must be remembered. Again, condition-action rules combined with the appropriate task set account for correct task performance.

Memorization

In a few studies, memorization has been used as a secondary task in recall (Depoorter & Vandierendonck, 2009). As explained previously, memorization requires a task set and is further governed by condition-action rules. When a memorization task is executed in the retention interval of another memorization task (with different contents), application of the condition-action rules matching WM contents completely accounts for controlled task execution.

In other words, existing dual-task research on the role of the central executive in WM has called on only reproductive-goal-achievement tasks, so there is no need to call on productive-goal-achievement actions. Although the present model accounts for productive-goal-achievement processes, in view of the kinds of tasks used to interfere with the central executive, one may ask whether productive-goal-achievement actions should also be part of the central executive. They are, no doubt, part of the cognitive repertoire, but is it necessary to assume that they are part of the executive control processes as needed in WM?

In an attempt to achieve a more restraining conceptualization of the central executive, Baddeley (1986) proposed that this agent corresponds to the supervisory attention system described by Norman and Shallice (1986). ⁸ Their model assumes two levels of control. As long as a well-trained skill is being executed, the system operates largely automatically; the occasional conflict is resolved semiautomatically on the basis of learned habits (contention scheduling). However, in novel situations or failures of the automatic conflict resolution, the supervisory attentional system comes into action. It intervenes in favor of one of the competing actions or can call on strategies for finding alternative solutions. The distinction between contention scheduling and supervisory attention seems to run parallel to the distinction made here between reproductive and productive goal achievement, although it is difficult to tell whether the two distinctions are completely equivalent. If this interpretation is correct, it follows that the present modeling can also account for actions subsumed by Norman and Shallice’s (1986) supervisory attention system. The remaining question of whether it is necessary to assume that WM functioning calls on supervisory attention and problem solving requires further research.

In the present proposal, I clearly have gone beyond a simple fractionation of the central executive into a restricted set of smaller components. Instead, I have tried to identify the processes underlying executive control. However, because the proposal is based on ideas from research on task switching, some may argue that the present modeling is representative of only one executive function: (task-)set shifting. Indeed, in the classification of executive functions proposed by Miyake et al. (2000), the latent variable of set shifting corresponds to the common variance in a number of task-switching contexts. However, the common variance among three variations of task switching might involve more than simply set shifting. In fact, the latent variable is defined as the commonality in task demands of the various task-switching contexts involved; as documented in the present article, this involves much more than replacing one intention by another one. Similarly, the latent variables of memory updating and inhibition also are defined as the commonality in a series of task demands. For memory updating, it concerns demands common to a number of memory-updating procedures (see also Szmalec, Verbruggen, Vandierendonck, & Kemps, 2011), and for inhibition, it concerns demands common to a number of situations in which an automatic response must be suppressed in favor of another response. Because the processes described in the present model include not only switching between tasks but also intentionally adapting memory contents (memory updating) and selecting some action sequences above other ones (selection and inhibition), it is clear that the model covers not only set shifting and task switching but also processes related to memory updating and inhibition.