Deductive Reasoning and WM’s Executive Functions

Deductive reasoning is a kind of thinking activity that has a precise starting point, a set of premises, and a goal: Drawing a conclusion; therefore, many researchers have considered it as a type of problem solving. In deduction, the conclusions do not involve any increase in semantic information. Also, the process of connecting premises to the conclusion is ruled by logic, that is, the conclusions have to be necessary and consistent. Deductive reasoning, even the most elementary kind, is hence a complex phenomenon that requires individuals to follow a sequential process that includes various steps and tasks and the passage from one to another. A second source of complexity comes from the need to temporarily store and update the diverse representations needed to carry out a deductive sequence. A third aspect is meta-deductive and consists of the necessity to keep track of this sequential process by keeping in mind the restrictions that rule deduction.

There are diverse theories of deduction, the two classical being that of “mental rules” and “mental models.” According to mental rules theories, people possess a set of rules, a sort of “natural logic” from which they reach a conclusion by following a sequence of steps. Reasoning proceeds thus in a derivation process in which people apply a series of rules and procedures that allows them to yield a conclusion (see Braine & O’Brien, Reference Braine, O’Brien, Braine, O’Brien and Braine1998; Rips, Reference Rips1994). Deduction is hence an effortful process that depends on the complexity of the deductive sequence and is therefore clearly affected by reasoners’ WM capacity.

The theory of mental models (the “model theory” for short) postulates that when individuals face deductive problems, they construct models or possibilities of the meaning of assertions consistent with what they describe (Johnson-Laird, 2008/Reference Johnson-Laird2012). The main assumption of the model theory concerns the crucial role of WM in deduction: Representing and manipulating models in order to reach a conclusion entail cognitive work and effort (Barrouillet & Lecas, Reference Barrouillet and Lecas1999). Therefore, reasoners are likely to base most of their inferences from the initial and incomplete representation or models of the premises. An inferential conclusion is necessarily valid if it holds in all the models of the premises. Finding a valid conclusion to complex problems requires that individuals build complete representations of premises and validate initial conclusions by searching for counterexamples that can make them false. In spite of their differences, rules and model theories agree that individuals’ WM capacity affects deductive process and conclusions.

A more recent conception is probabilistic or suppositional theory on conditional reasoning (Evans & Over, Reference Evans and Over2004; Oaksford & Chater, Reference Oaksford and Chater2003; Oberauer & Wilhem, Reference Oberauer and Wilhelm2003; for a recent review and proposal see Oaksford & Chater, Reference Oaksford and Chater2020). This theory considers that the conditionals cannot be interpreted in truth-functional terms, that is to say their truth does not depend on the values of their component propositions as they are represented in the truth table, whether this is that of material implication or that of equivalence or biconditional. A conditional “If Antecedent then Consequent” is not understood as true or false but is understood as more or less credible or probable, and its probability is defined as the probability that the consequent is given, once the antecedent is given: P(Consequent/Antecedent). According to suppositional theories, conditional reasoning relies on a likelihood estimate process that consumes WM resources. But these WM demands are mainly based in connecting with information stored in LTM. There is not a high demanding process as the searching for counterexamples. Therefore, the reasoning process relying on suppositional theories does not require WM resources as heavily as does the reasoning process based on the construction of mental models and the search for counterexamples (Verschueren et al., Reference Verschueren, Schaeken and d’Ydewalle2005).

As we have seen, with nuances and peculiarities, the cognitive theories of deduction highlight the function that WM has in reasoning. Apart from these reasoning theories, there is a general theoretical approach on thinking and reasoning in which the role of WM and executive processes is crucial: Dual-process theories (see, Evans, Reference Evans2008; Evans & Stanovich, Reference Evans and Stanovich2013; Kahneman, Reference Kahneman2011; Kahneman & Frederick, Reference Kahneman, Frederick, Gilovich, Griffin and Kahneman2002; Sloman, Reference Sloman1996). These theories postulate the existence of two different types or processing systems of thinking: System 1 (intuitive) and System 2 (deliberative). System 1 is considered fast, unconscious, associative, and not dependent on WM. System 1 allows individuals to quickly access intuitive responses that can be valid, but it is also a source of pervasive mistakes. On the other hand, System 2 is slow, conscious, controlled, and strongly linked to reasoners’ WM as well as their thinking dispositions or mental styles. WM is thus a defining feature of analytical System 2.

System 2 is required to solve complex reasoning problems, although this is not a sufficient condition for valid responses. Most dual-processing theories assume System 1 yields intuitive responses that subsequent System 2 deliberation may or may not modify. Stanovich et al. (Reference Stanovich, West and Toplak2011) claim that deliberative reasoning requires override System 1 processing. Overriding System 1 and activating System 2 processing require an individual’s executive control, as well as a propensity to think actively and resist the premature closing of problems. Executive control processes thus play a crucial role in analytical System 2 reasoning processes (see De Neys & Glumicic, Reference De Neys and Glumicic2008; Evans, 2009/Reference Evans, Evans and Frankish2012; Thompson, 2009/Reference Thompson, Evans and Frankish2012). From a mental model perspective, García-Madruga et al. (Reference García-Madruga, Gutiérrez, Carriedo, Luzón and Vila2007) highlighted that the central executive was the crucial WM component in the explanation of propositional reasoning performance. In order to confirm the role of executive processes in deductive reasoning, these authors used two WM central executive measures: the classical Reading Span Test (RST) (Daneman & Carpenter, Reference Daneman and Carpenter1980), in which people have to remember the final word of a series of sentences; and a new test that loads more on the central executive since it demands that people solve and remember the word solutions to a series of verbal anaphora. These authors found that higher WM participants, as opposed to lower WM participants, gave reliably more correct System 2 responses and fewer intuitive (System 1) responses to the deductive problems, particularly on the new more complex anaphora measure. Likewise, studies with syllogistic reasoning problems have borne out the crucial role of WM, particularly the executive processes (see Capon et al., Reference Capon, Handley and Dennis2003), as well as its relationship with the two types of reasoning processes (see Gilhooly et al.,Reference Gilhooly, Logie and Wynn1999).

The role of executive processes, particularly inhibition, has been also pinpointed in the well-known Wason selection task. In this task four cards (A, P, 7, 2) with a letter on the one side and a number on the other side, people are asked to turn over the cards that falsifies the rule: “If there is a vowel on the one side, then there is an odd number on the other side.” People usually choose A and 7. This bias is called the perceptual matching bias because people choose the mentioned items (Evans, Reference Evans1989; Evans & Lynch, Reference Evans and Lynch1973); however, the correct answer is A and 2, that is, people need to inhibit their first answer and redirect attention to the alternative response. Houdé et al. (Reference Houdé, Zago, Mellet, Moutier, Pineau, Mazoyer and Tzourio-Mazoyer2000) ran an inhibition control training session to avoid the matching bias and found a shift of brain activation using a positron emission tomography (PET) scan from the posterior part of the brain on the pretest to a left prefrontal network on the posttest; that is, from perceptual-related areas to WM-related areas. According to Houdé and Borst (Reference Houdé and Borst2015), learning to inhibit misleading heuristic responses from System 1 and activate the logical algorithms of System 2 is the critical course of action that allows a person to reason logically (see also Stanovich et al., Reference Stanovich, West and Toplak2011); however, this capacity is highly dependent on the maturation of the prefrontal cortex.

From the dual-process theory, metacognitive processes have been highlighted by Thompson and colleagues. According to Thompson et al. (Reference Thompson, Prowse Turner and Pennycook2011), System 1 processes are accompanied by a metacognitive experience, called the feeling of rightness (FOR), that is, the confidence in one’s intuitive responses which can signal when additional System 2 analysis is needed. They found a robust relationship between the low FOR and the activation of System 2. More recently, Bago et al. (Reference Bago, Raoelison and De Neys2019) tried to activate System 2 thinking using a second guess (two-response) paradigm in the bat-and-ball problem:

This problem is included in the cognitive reflection test developed by Frederick (Reference Frederick2005) that allows evaluating individuals’ ability to override System 1 processes and be able to give a hard System 2 response. Bago et al. (Reference Bago, Raoelison and De Neys2019) asked participants to give a first answer to this problem and rate the confidence in their own responses. The most probable response was the intuitive answer “10 cents”. Participants were also less confident in their incorrect responses than the correct ones. In a second guess, in which participants were allowed to give a second response to the problem, they made fewer mistakes than in the first attempt. Also, they gave responses smaller than the intuitive “10 cents” getting closer to the correct answer “5 cents.” According to the authors, although biased reasoners did not know the exact correct answer, they knew the right answer should be smaller than the intuitively biased response. As we can see, the low confidence in the intuitive responses is based on partial insight into the nature of one’s error. These results confirm the role of the FOR and highlight the importance of metacognition in the searching for System 2 responses (Ackerman & Thompson, Reference Ackerman and Thompson2017).

A second important result of the two-response paradigm is the existence of intuitive logical responses (Bago & De Neys, Reference Bago and De Neys2017). These authors examined the time course of dual-process theory and used time pressure and/or cognitive load to make sure that the initial response was really intuitive. They asked participants in the initial stage of a two-response paradigm to respond as fast as possible with the first intuitive answer that comes to mind. In the second stage of response, participants were allowed to generate their response taking all the time they want. The authors confirmed that reasoners were frequently able to give correct, logical responses in the first stage. Moreover, these initial correct responses were fast and high confident, and were given in the face of conflicting heuristic responses. The obvious conclusion is that some participants facing difficult deductive problems may be able to give fast intuitive responses that are correct and logical.

The existence of intuitive logical responses has been confirmed using other experimental paradigms and has induced the proposal of a revised 2.0 dual process theory (see De Neys, Reference De Neys2018; De Neys & Pennycook, Reference De Neys and Pennycook2019). According to new proposal multiple types of intuitive responses will be cued simultaneously (De Neys, Reference De Neys2012; Pennycook et al., Reference Pennycook, Fugelsang and Koehler2015), ones emerging from the traditional superficial and beliefs bias, and others from an acquired knowledge of some basic logical principles. The different available intuitions can vary in their strength or activation level. When two intuitive responses of similar strength are cued by System 1 processing, a conflict between them is likely detected, and the deliberate System 2 processing is called on (Pennycook et al., Reference Pennycook, Fugelsang and Koehler2015). The deliberate processing can then be used to override the dominant intuitive response, but it also can be used only to verify or rationalize it (García-Madruga, Reference García Madruga1983; Pennycook et al., Reference Pennycook, Fugelsang and Koehler2015).

Logical intuitions are most likely the result of the automatization mechanism that underlies learning and characterize the transition from novel to expert knowledge and abilities in diverse fields (Shiffrin & Schneider, Reference Shiffrin and Schneider1977). The deliberate-to-intuitive automatization process has long been recognized by dual-process theories. According to Kahneman and Frederick (Reference Kahneman, Frederick, Gilovich, Griffin and Kahneman2002, p. 3), “complex cognitive operations can migrate from System 2 to System 1 as proficiency and skill are acquired.” These authors mention as typical example the capacity of chess masters to perceive the strength or weakness of chess positions instantly as a kind of automatized System 1 ability. Similarly, prolonged exposure to mathematical and deductive tasks at school would be in the origin of logical intuitions.

But logical intuitions are not the most important acquisition of the deductive learning process included in the instructional procedure presented in this paper. Our main aim is the acquisition of the capacity to identify, inhibit and override biased intuitions, by means of the applying of an entire deliberating process.

Our proposal maintains that in order to teaching people how to deal with complex deductive tasks it is necessary to instruct and train them on how to apply during the searching of solution the main EFs involved: (a) To focus attention and activate all cognitive resources; (b) to switch attention from one cognitive task to another, that is, to pass from one step to the next in a deductive sequence; (c) to activate and use knowledge stored in LTM in order to update WM representations and access to connected logical knowledge; (d) to inhibit initial intuitive responses and discard irrelevant information; and (e) to revise intuitive responses in a controlled metacognitive way, overriding the biased ones and confirming the logical ones. Apart from these main EFs, but closely related with them, the unfamiliarity and difficulty of deductive tasks may lead reasoners to get stressed and run off from the task. Emotional control is hence a sixth EF that has also to be trained. For this reason, we propose to include all of these EFs in an integrative reasoning training procedure. Our training procedure will be focused on learning the main deductive and metadeductive principles which allow the correct understanding and revision of deductive statements and problems, as well as the emergence of logical intuitions. But before presenting our intervention procedure we need to analyze the recent advances in the field of cognitive training in which our intervention is based.

Cognitive Training and the Improvement of Higher-Level Cognitive Abilities

Initial work focused on reasoning trainability has evidenced that formal training and teaching can improve inferential abilities (e.g., Cheng et al., Reference Cheng, Holyoak, Nisbett and Oliver1986; Nisbett et al., Reference Nisbett, Fong, Lehman and Cheng1987). Over the last few decades, research on the potential of cognitive training in different areas of cognition, including reasoning (Ariës et al., Reference Ariës, Groot and den Brink2014), has been growing (see, e.g., Strobach & Karbach, Reference Strobach and Karbach2016). Previous studies focused on induced cognitive and neural plasticity have evidenced the impact of training on both the structure and functioning of neural networks (Barnes et al., Reference Barnes, Woolrich, Baker, Colclough and Astle2016). Consistent with this view, the effectiveness of cognitive training interventions is hypothesized and discussed. There are different approaches to executive functioning training. Recent review by Diamond and Ling (Reference Diamond, Ling, Novick, Bunting, Dougherty and Engle2020), including computerized and non-computerized cognitive training, neurofeedback, school programs, physical activities, mindfulness practices, suggests that both noncomputerized cognitive training and school programs show better results than computerized training to improve EFs.

Most interventions aimed at improving WM and EF are based on the design and application of a process-based WM training regimen (i.e., training of specific cognitive processes without explicit strategy training) based on intensive and systematic practice of complex WM tasks (e.g., Cogmed Working Memory Training Program; Klingberg et al., Reference Klingberg, Fernell, Olesen, Johnson, Gustafsson, Dahlström, Gillberg, Forssberg and Westerberg2005). The results of different systematic reviews on the effectiveness of this type of intensive and systematic cognitive WM training programs indicate that they improve the performance on the trained tasks and other untrained WM tasks that share features close to those of the trained tasks (see Klingberg, Reference Klingberg2010; Melby-Lervåg et al., Reference Melby-Lervåg, Redick and Hulme2016; Soveri et al., Reference Soveri, Antfolk, Karlsson, Salo and Laine2017). Positive effects were found in school-aged children, and adolescents with typical development (for review, Karbach & Unger, Reference Karbach and Unger2014; Melby-Lervåg & Hulme, Reference Melby-Lervâg and Hulme2013), but also up to adulthood (Karbach & Verhaeghen, Reference Karbach and Verhaeghen2014). Positive effects were also found with students with cognitive deficits (Dunning et al., Reference Dunning, Holmes and Gathercole2013) or learning difficulties (Titz & Karbach, Reference Titz and Karbach2014). However, recent reviews (Sala & Gobet, Reference Sala and Gobet2017, Reference Sala and Gobet2020) suggest that the transfer effect of WM training to other cognitive abilities (fluid intelligence, academic skills, reading, or mathematics) is zero or, when observed, is minimal in typically developing school-children aged between 3 and 16 years.

Hence, the core question to be elucidated is what conditions give rise to the possible transfer following WM and EF training. In that respect, two main proposals both restraining widely the capacity of transfer are posed. One hypothesis is that WM training enhances the specific processes within WM that are engaged by particular tasks: a process-specific transfer view. Consequently, transfer should only be expected when trained and untrained tasks both place demands on the same processes (see, von Bastian & Oberauer, Reference von Bastian and Oberauer2014). A second more restrictive perspective proposed by Gathercole et al. (Reference Gathercole, Dunning, Holmes and Norris2019) maintains that transfer from WM training is a consequence of the development of new routines that must be implemented to accomplish a mental activity and are applied to new tasks. In other words, transfer only occurs when individuals have learned a new complex cognitive skill in the course of training and when that skill can be applied to a novel task with similar structure. The new “routine” is needed to execute the precise sequence of cognitive processes when a task has complex and unfamiliar cognitive requirements.

On a more particular note with respect to a domain-specific training, some additional evidence comes from studies analyzing increased reasoning scores following different forms of WM training, particularly the specific impact of strategy-based WM training on reasoning. Ariës et al. (Reference Ariës, Ghysels, Groot and van den Brink2017) reviewed literature and concluded that there is no convincing evidence that content-based WM training alone (e.g., n-back training) improves adolescents’ reasoning skills in education. However, training that combines both content-based WM-capacity and reasoning-strategy could serve as an effective instrument to enhance school-based reasoning achievements.

For our purposes, we will focus on those cognitive training programs integrated into the school curriculum itself, so that the training is carried out in the social setting of classroom and in the context of learning tasks in which EFs are required (see Barnes et al., Reference Barnes, Woolrich, Baker, Colclough and Astle2016; Meltzer et al., Reference Meltzer, Pollica, Barzillai and Meltzer2007). As mentioned above, previous findings indicate that school cognitive training programs showed mildly better results than computerized approaches at improving EFs measures (see Blair & Raver, Reference Blair and Raver2014; Diamond & Ling, Reference Diamond, Ling, Novick, Bunting, Dougherty and Engle2020). Although there are still scarce studies that try to improve EF in the context of learning activities that can be part of the curriculum, the results promise to enhance academic skills in the domain of mathematics problem-solving (Swanson, Reference Swanson2015), reading comprehension (García-Madruga et al., Reference García-Madruga, Elosúa, Gil, Gómez-Veiga, Vila, Orjales, Contreras, Rodríguez, Melero and Duque2013), and reasoning (Ariës et al., Reference Ariës, Groot and den Brink2014).

Our theoretical view maintains that an effective way to improve higher-level cognitive abilities by WM training would be through the design and implementation of instructional programs that explicitly emphasize the activation of the WM’s online core EFs—the general domain component of EC—in the context of new and complex cognitive tasks that involve executive functioning in a specific domain (e.g., arithmetic, Sánchez-Pérez et al., Reference Sánchez-Pérez, Castillo, López-López, Pina, Puga, Campoy, González-Salinas and Fuentes2018; reading comprehension, García-Madruga et al., Reference García-Madruga, Elosúa, Gil, Gómez-Veiga, Vila, Orjales, Contreras, Rodríguez, Melero and Duque2013; reasoning, Ariës et al., Reference Ariës, Groot and den Brink2014; see also Gobet & Sala, Reference Gobet and Sala2022). We share the idea that there is a general mechanism underlying the transfer from complex WM tasks to higher-level cognitive abilities such as reasoning, but we claim that there is also a specific mechanism bounded to the use of concrete tasks in the diverse fields. Thus, the activation of the specific mechanism involves both analyzing the role of EFs in the selected higher-level thinking ability and selecting a set of relevant tasks to train in the higher-level thinking field. Hence, our approach could also be aligned with the cognitive training as skill acquisition hypothesis (Gathercole et al., Reference Gathercole, Dunning, Holmes and Norris2019) given that we attempt to improve higher-level thinking abilities (e.g., deductive reasoning) through WM and EF training during the carrying out of new and complex reasoning tasks. This aspect is an essential difference with respect to training programs particularly focused on intensive and systematic practice of complex WM tasks. The second main feature is that our training perspective is close to an ecological vision of cognitive training applied to education (Moreau & Conway, Reference Moreau and Conway2014). According to this view, the training proposal integrates complexity, novelty, and diversity to maximize ecological validity. This means that students will be engaged in complex and novel activities that combine diverse cognitive demands, as noted, and have real-world applications; meanwhile the program is designed to be implemented in educative natural classroom settings.

Overall, the findings suggest a promising line to design training programs for improving WM and EFs. Executive functioning training appears to transfer in some conditions, even though transfer appears to be narrow and some important questions remain. As Diamond (Reference Diamond2013; Diamond & Ling, Reference Diamond and Ling2016, Reference Diamond, Ling, Novick, Bunting, Dougherty and Engle2020) pointed out, a few principles seem to hold for effective training: (a) WM and EFs can be improved at any age through cognitive training and practice; (b) EF gains seem to depend on the amount of repeated practice; (c) EFs need to be continually challenged by training programs that keep incrementing task difficulty progressively as a person’s skill improves; and (d) often those with the poorest EFs consistently gain the most from any program that improves EFs. Our view justifies the promotion of controlled processes using a metacognitive approach. In this way the participants would receive guidance in order to recognize the existence of control processes in the training program activities, as well as to think about and be aware of their importance.

In this vein, in the next section of this paper, we propose a training program with specific activities that have a relevant content for secondary students, for instance, fallacies in ordinary context, false beliefs of individuals, and fake news.

This part has allowed us to substantiate four main basic questions concerning to how to intervene. According to our review, our intervention program will not be a typical program of training WM and EF tasks to improve reasoning abilities, as it will be based on the improvement of WM and EF during and within the process of solving deductive and metadeductive tasks. Nevertheless, direct training of WM and EF has also an important role in our training method: Following Gathercole’s (Reference Gathercole, Dunning, Holmes and Norris2019) view, the training of WM complex tasks implies to develop and practice diverse mental subroutines that are also involved in deductive and metadeductive tasks. As a matter of fact, complex WM and deductive reasoning share the need to activate the same core executive processes to solve tasks that demand reasoners to build and integrate multiple representations to draw inferences and remember the final result of a sequential thinking process. Our intervention program will apply the above effective training principles highlighted by Diamond and, likewise, it will be integrated in the context of learning activities at classroom.

A Metacognitive Training Procedure to Improve Deductive Reasoning

The development of reasoning seems to be closely related to the development of WM and executive processes (see, e.g., Camos & Barrouillet, Reference Camos, Barrouillet, Camos and Barrouillet2018). With age, children are increasingly able to understand and infer valid conclusions from propositional assertions. According to the model theory, the developmental pattern is related to the number of true possibilities contained within each assertion: children first interpret conjunctions, and then disjunctions and conditionals. First defended by the model theory, this pattern of acquisition is directly related to an increase in WM capacity during childhood and adolescence (see Johnson-Laird, Reference Johnson-Laird, Butterworth and Bryant1990; Johnson-Laird et al., Reference Johnson-Laird, Byrne and Schaeken1992; see also Barrouillet & Lecas, Reference Barrouillet and Lecas1999; Santamaría et al., Reference Santamaría, Tse, Moreno-Ríos and García-Madruga2013).

Due to its special relevance, researchers have paid particular attention to the development of conditionals. Children’s interpretation of conditionals, such as “If it rains then Eliza uses an umbrella,” seems to be based mainly on the construction of only one true possibility, the initial one that affirms both clauses: the antecedent and the consequent (it rains and Eliza uses umbrella); conditionals are thus interpreted as conjunctions. Older children and preadolescents are also able to construct and use a second possibility in which the antecedent and the consequent are negated (it does not rain and Eliza does not use umbrella); that is, at this age, most individuals make a biconditional interpretation of “if” assertions. Finally, only late adolescents and adults are able to build the third true conditional possibility which negates the antecedent and affirms the consequent (it does not rain and Eliza use umbrella). A complete interpretation of conditionals is thus a late developmental acquisition, particularly with abstract premises (see, e.g., Barrouillet et al., Reference Barrouillet, Grosset and Lecas2000; Markovits, Reference Markovits2000; Markovits & Barrouillet, Reference Markovits and Barouillet2002; Rojas-Barahona et al., Reference Rojas-Barahona, Moreno-Ríos and García-Madruga2010).

A similar developmental pattern was found in the interpretation and reasoning from syllogistic premises with abstract content by García-Madruga (Reference García-Madruga1982). In this study, students of four academic levels (seventh graders, ninth graders, eleventh graders, and first year university students) were asked to interpret the four syllogistic premises by means of Euler diagrams. They were also asked to solve a set of syllogistic problems of various difficulties. The percentage of mistaken interpretations of the four types of syllogistic premises decreased with age, from seventh graders (12 years old) to university students (18.9 years old), although the percentage of incomplete representations (i.e., correct but not complete responses) was very high in both adolescents and adults. For instance, only a half of adolescents (eleventh graders, 16.5 years) and young adults (university students,) were able to correctly interpret universal affirmative assertions, such as “All A are B.” The percentage of correct responses in the syllogistic reasoning task also increased with age, although the most difficult problems (i.e., those that demands exhaustivity and require searching for counterexamples) were also very difficult for older students.

WM’s capacity is not, however, the only variable that explains the development of reasoning abilities throughout childhood and adolescence. As Inhelder and Piaget (Reference Inhelder and Piaget1955) claimed, there are some specific changes in reasoning abilities during preadolescence and early adolescence, between 12 and 15 years: The acquisition of formal thought would be the result of a complete and prolonged in time period of school learning. Formal operations were explicitly characterized by Inhelder and Piaget (Reference Inhelder and Piaget1955) as deductive reasoning abilities. Thinking does not require concrete or real situation but works in an abstract way, in the possible world, by means of propositional statements and hypotheses that can be exhaustively checked. As we can observe, the acquisition of formal thinking would imply the emergence of logical intuitions.

The connection between formal operational thought and logical intuitions may be explained from the concept of metalogical or metadeductive knowledge and abilities and its development. According to Moshman (Reference Moshman and Overton1990; Reference Moshman2011), the new deductive abilities acquired in the stage of formal operations by adolescents must be interpreted as metalogical or metadeductive. They involve an individual’s capacity to reflect on one’s own logical activity itself and to distinguish between logical validity and reality. Metadeductive abilities include the implicit understanding of the logical system and its basic concepts of necessity and validity, as well as the explicit use of this knowledge by applying metalogical strategies, such as searching for counterexamples. There is a gradual acquisition of metalogical awareness during preadolescent and adolescent years: from 11 to 12 years, preadolescents begin to understand the concepts of necessity, consistency, and the validity of logical conclusions (Markovits et al., Reference Markovits, Thompson and Brisson2014; Santamaría et al., Reference Santamaría, Tse, Moreno-Ríos and García-Madruga2013). However, preadolescents and adolescents cannot think about the logical system as a whole and take it as an object of knowledge. Explicit metalogic capacity only becomes possible in late adolescence and adulthood when individuals are already able to apply metadeductive strategies in solving deductive problems. This late acquisition is unsurprising since these strategies involve applying the metadeductive concepts of necessity and consistency. This application is mostly difficult and demands the activation of the EFs. Searching for counterexamples is a deliberation process that implies both metadeductive concepts trying to falsify an initial conclusion. Exhaustivity also demands to apply both concepts in a task requiring high motivation and the avoiding of a premature close. The correct applying of these interrelated concepts and strategies will allow reasoners to solve any type of deductive problems.

Velasco and García-Madruga (Reference Velasco and García-Madruga1997) investigated the development of metalogical understanding and logical reasoning using abstract syllogistic premises during preadolescence and adolescence (between seventh and twelfth graders). They confirmed that a third of seventh graders (12.5 years old) were still unable to understand the logical concepts of necessity and validity correctly. Likewise, these authors found that only a half of twelfth graders (17.8 years old) used the strategy of searching for counterexamples spontaneously.

Given the developmental pattern we have briefly described, we may conclude that an instructional program on WM executive processes to achieve a global improvement of deductive reasoning and generate a general understanding of basic deductive and metadeductive concepts and abilities cannot be applied before adolescence. A successful earlier intervention on deduction is possible but limited to specific inferential rules and schemes and focused solely on the metacognitive acquisition and use of basic logical concepts, as Christoforides et al. (Reference Christoforides, Spanoudis and Demetriou2016) have demonstrated through the implementation of a training program on conditional inferences for children between the ages of 8 and 11 years.

Our theoretical explanation on the relationship between EFs and thinking allows us to design a procedure for training deductive reasoning with adolescents. A first step in deduction is to reach the correct interpretation of premises, that is, to build a correct representation of premise meaning. The comprehension of premises is not specific to reasoning, but the goal-oriented sequential task of manipulating representations in order to arrive at a necessary conclusion is. This sequential task is performed in WM and can be defined as a specific kind of updating process. It is not driven by the input, as in the case of ordinary reading comprehension, but instead is a top-down updating process driven by reasoners’ meta-deductive concepts and abilities. This meta-deductive knowledge includes the following tenants that: (a) Premises and conclusions must be consistent; (b) a valid conclusion must be necessary; (c) a useful strategy to reach a valid conclusion is one of searching for counterexamples; and (d) when looking for a necessary conclusion, reasoners should never quit before evaluating all the possibilities (i.e., their work must be exhaustive). In order to reach a valid conclusion in complex reasoning problems, individuals have to carry out a sequential top-down updating process that includes the following stages (see Johnson-Laird & Byrne, Reference Johnson-Laird and Byrne1991; see also Fangmeier et al., Reference Fangmeier, Knauff, Ruff and Sloutsky2006):

1. Comprehension of premises. Reasoners have to understand deductive premises in depth. They should search for and be aware of the different possibilities of the meaning of sentences. These possibilities must be consistent.

2. Integration of premises and formulation of an initial conclusion. This initial intuitive conclusion is likely not necessary; it is based only on a partial set of possibilities. Reasoners have to recognize that this initial response is likely invalid and therefore they should inhibit it. Some individuals can have a logical correct intuition which is likely correct, but it has also to be validated.

3. Validation. This revision phase is particularly important, and it takes time and can be very demanding from a cognitive and motivational perspective.

3 a. Applying a strategy of searching for counterexamples involves activating LTM knowledge, using diverse possibilities of the meaning of sentences, and combining these possibilities in order to falsify the initial conclusion.

3 b. Validation may be completed in two cases only: (a) A new conclusion without counterexamples has been found; and (b) An exhaustive analysis of the meaning of sentences does not find a necessary conclusion.

The four main objectives of the training program are to improve reasoners: (a) Comprehension of deductive assertions and premises; (b) metadeductive knowledge and revision strategies; (c) inhibitory control to avoid intuitive responses and a premature closure of the task; and (d) metacognitive control and monitoring of the updating process by means of explicit instruction and repeated practice to automatize the applying of metadeductive concepts and strategies. This fourth objective also includes the emotional control of the training tasks during the applying of program. The program is designed to be applied to 15–16 years old adolescents (tenth grade level) and consists of 12 sessions of 50 min, and eight different tasks (see Table 2). The first session focuses on explicitly laying out the theoretical basis of the instructional program, that is, the role of executive and metacognitive processes in reasoning. The presentation of the trained EFs is illustrated with a specific icon for each executive process (see Table 3). In this first session, we explain the sequence of deduction, the role of diverse executive processes including emotional control of the task, the difference between deduction and metadeduction, and the importance of metacognitive awareness of deduction.

Table 2. Description of Sessions and Training Tasks in the Deductive Reasoning Program

Table 3. The Executive Processes Trained, Their Icons, and Reasoning Phases (in Italics) and Tasks

We also present the FOR perspective in the activation of System 2 and the identification of fallacies: When the FOR is low, System 2 tends to activate. As being a result of automatization, logical intuitions would have a high FOR, and System 2 processes would not likely need to activate. This perspective has an interesting instructional corollary: To improve the activation of System 2 training must include instructional experiences that diminish people’s FOR when facing fallacies. Likewise, we present the concept of logical intuitions and how to automatize metadeductive principles to get them. The following is an example of the specific reasoning contents:

Pablo is not very good in Maths. Isabel, his teacher, has told him: “if you work harder then you will pass the exam.” In summertime, after the end of exams, we met Pablo and asked him whether he passed the mathematics exam or not. He told us: “The teacher is a liar, I did not work harder but I passed” What do you think? Is the teacher a liar? Why?

To solve this example participants will have to identify the “negation of antecedent” fallacy in a conditional “If A then B”. Pablo committed this fallacy when considers that Isabel is a liar. According to this fallacy, when the antecedent is negated “I did not work harder,” the only true possibility is the negation of the consequent “I did not pass the exam,” therefore “I did not work harder and I passed the exam” is considered false, however this is wrong. Participants in our training program faced to this example will probably have a low FOR in this fallacy. Training work will have as objective to identifying and overriding the “negation of antecedent” fallacy, that is, to acquire a logical intuition against this fallacy.

The final session of the program is that of recapitulation: The main aspects of training as well as its utility for diverse situations and intellectual contexts are described and discussed with participants. Among a few of these contexts, practical examples are presented on daily situations, politics, argumentation, and academic subjects in the social and natural sciences, and that of mathematics.

The training tasks used in the program are three WM tasks and five reasoning tasks. At the end of these tasks a brief assessment of possible emotional troubles is carried out. All the training sessions, except the first and last ones, end with a short reasoning task that presents to secondary students some basic fallacies to be identified, as well as various activities relevant to their interests, such as Sudoku, detective games, and detecting fake news.

The instructional techniques are the same as those used in the reading comprehension program designed by García-Madruga et al. (Reference García-Madruga, Elosúa, Gil, Gómez-Veiga, Vila, Orjales, Contreras, Rodríguez, Melero and Duque2013): Direct instruction, modeling, and guided and independent practice. The three WM tasks are the analogy, anaphora, and operation tasks. In these tasks, participants must solve a series of verbal analogies, anaphora, or simple arithmetic problems and remember the solution to each of them. These tasks are complex dual tasks that involve the repeated operation of solving an inferential problem, as well as storing and maintaining activated in WM its solution. Therefore, WM tasks require the activation of the four core executive processes: Participants must focus and switch attention, update and connect to LTM to infer the solution to be remembered, and to inhibit wrong responses to the inference task. Most importantly, these WM tasks possess a very similar structure to reasoning tasks. Although a more precise analysis would be necessary, we think that these tasks probably involve some of the cognitive routines also included in deductive reasoning tasks (see Gathercole et al., Reference Gathercole, Dunning, Holmes and Norris2019).

In reasoning tasks, we use an adaptive learning procedure, that is, in each task, problems are presented in an increasing order of difficulty. This adaptive procedure is certainly important because promotes motivation and reduce the emergence of emotional control troubles. Participant’s behavior throughout each task is recorded. The four core executive processes are involved in each of the training tasks and problems. Moreover, the sequential task of drawing valid deductive inferences requires the active monitoring of the reasoning process, inhibiting a premature closing of the task and revising any conclusions reached. In Table 3, the involvement of diverse EFs in each stage and task of reasoning can be observed. As mentioned above, the five reasoning tasks, particularly Task 5, include activities that address issues, contexts and contents of specific interest for secondary students, such as fallacies, Sudoku, fake news, etc. An example of task to work the main reasoning tasks (consistency, necessity, exhaustivity and searching for counterexamples) would be:

Is this conclusion (a) possible; (b) impossible; (c) necessary true?

In this task, people are asked to select the correct response. To resolve this problem properly, they need to search counterexamples that falsify this conclusion. As there is not an alternative conclusion, then the conclusion is necessarily true.

A second example would be:

In this case, the conclusion is not necessary, just possible, because there is another alternative conclusion, e.g., “it does not rain, and she uses umbrella.” In the next example, the conclusion is impossible because it is not consistent with premises, that is, it does not follow from them. For example:

This type of tasks allows us to work on the main concepts that are important to think rationally and not fall into intuitive answers. People learn to exhaustively represent the possibilities, not just the first possibility that comes to mind, as well as to look for counterexamples and infer whether the conclusion is consistent or inconsistent with the premises, and therefore determine whether the conclusions are necessary, possible or impossible. As Johnson-Laird (Reference Johnson-Laird, Wegerif, Li and Kaufman2015) has highlighted, the key for improving thinking is to represent the highest number of possibilities. As the model theory has showed, one of the most persistent phenomena in deductive reasoning is the presence of illusions (see Khemlani & Johnson-Laird, Reference Khemlani and Johnson-Laird2017). According to this theory, these errors are made because people tend to represent just the initial models. Our prediction is that the present intervention program should be efficient to reduce these illusions by helping people to bear in mind as many alternatives as possible, not only the initial models, and also to search for counterexamples.