Elsevier

Neuropsychologia

Volume 47, Issue 4, March 2009, Pages 1107-1116
Neuropsychologia

Cortical bases of elementary deductive reasoning: Inference, memory, and metadeduction

https://doi.org/10.1016/j.neuropsychologia.2009.01.004Get rights and content

Abstract

Elementary deduction is the ability of unreflectively drawing conclusions from explicit or implicit premises, on the basis of their logical forms. This ability is involved in many aspects of human cognition and interactions. To date, limited evidence exists on its cortical bases. We propose a model of elementary deduction in which logical inferences, memory, and meta-logical control are separable subcomponents. We explore deficits in patients with left, medial and right frontal lesions, by both studying patients’ deductive abilities and providing measures of their meta-logical sensitivity for proof difficulty. We show that lesions to left lateral and medial frontal cortex impair abilities at solving elementary deductive problems, but not so lesions to right frontal cortex. Furthermore, we show that memory deficits differentially affect patients according to the locus of the lesion. Left lateral patients with working memory deficits had defective deductive abilities, but not so left lateral patients with spared working memory. In contrast, in medial patients both deductive and meta-deductive abilities were affected regardless of the presence of memory deficits. Overall, the results are compatible with a componential view of elementary deduction, and call for the elaboration of more fine-grained models of deductive abilities.

Introduction

Being able to grasp the deductive relations among sentences or thoughts is a fundamental cognitive ability. If you want to go to a movie and your friend says that if it rains she will not come, and then if it does rain, you will not wait for her. Successful exchanges of information among people, or planning of novel action sequences, require the ability to carry out such deductive inferences: our everyday mental life is densely populated by them.

Deductive reasoning is often much more complex. It is involved in mathematics, formal logic, categorization, and scientific hypothesis testing and confirmation. Yet, while most people will never engage in sophisticated logico-mathematical reasoning in their life, the kind of everyday reasoning we exemplified above is arguably universal. As basic deductive steps are also involved in word learning (Halberda, 2003), elementary reasoning is also likely to appear early in development. By contrast, most mathematical or sophisticated logical reasoning requires years of training and appears late in life. Different levels of performance also support the contrast between the two types of deductive abilities. While humans solve simple deductive problems involved in everyday reasoning almost flawlessly (e.g. Braine, Reiser, & Rumain, 1984), once they go beyond this level of elementary reasoning errors abound. The relations between early basic reasoning abilities and the more sophisticated ones, such as explicit logico-deductive or mathematical reasoning, are unclear. However, what is apparent is that deductive reasoning is a multi-faced phenomenon, not necessarily involving only a single psychological mechanism. In this article, we will concentrate on the basis of elementary reasoning abilities, that is, the deductive abilities that every human being possesses and deploys in everyday exchanges of information.

An elementary level of deductive inference is presupposed by both main theories on human deduction – mental models and mental logic – along with more sophisticated reasoning abilities. According to mental logic theory, reasoning involves the construction of short mental proofs, built by means of a set of rules and procedures for their application. According to one of the most developed version of this theory (e.g., Braine & O’Brien, 1998a), reasoners possess rules in natural deduction form that govern the introduction or elimination of connectives and quantifiers. A procedure for the application of those rules (called Direct Reasoning Routine, hereafter DRR) allows reasoners to move from premises to conclusions in a finite number of steps. The set of natural deduction rules and its associated DRR are meant to describe the universal elementary reasoning skills. In contrast, complex abilities responsible for individual differences depend on the acquisition of secondary reasoning strategies. These are not primitive, do not appear early in development, and not everybody develops them. Critically, it is assumed that they require the involvement of cognitive processes qualitatively different from the ones involved in elementary reasoning. Evidence consistent with the mental logic theory of elementary reasoning has been found in abstract problem solving (Braine et al., 1995), proof understanding, text understanding, memory for stories and lexical retrieval (Lea, 1995, Lea et al., 1990), almost exclusively within the domain of propositional reasoning.

In the mental model framework, a clear distinction between primary and secondary reasoning is not so explicit, but it is still present. The mental model theory holds that reasoning consists in the construction of analogical structures that mirror real states of affairs (e.g., Johnson-Laird, 1983, p. 419; Johnson-Laird & Byrne, 1991). In contrast with the mental logic theory, such structures do not require rule-like logical operations, or the explicit representation of variables or quantifiers: the ability to represent examples of real states of affairs grounds reasoning. Besides reasoning proper, the mental model theory also aims at explaining understanding and text comprehension (Johnson-Laird, 1983, Garnham, 1987). According to the theory, understanding a conversation, or a text, or a set of premises, means to build a first model consistent with it (Johnson-Laird & Byrne, 1991). This first step of comprehension is spontaneous and automatic. By contrast, the creation of further alternative models consistent with the premises or text (which are necessary to undertake more sophisticated reasoning) requires effort, motivation, and is severely limited by memory resource allocations. Thus, within the mental model theory, the difference between first comprehension and construction of alternative models grounds the difference between an intuitive level of model construction involving the creation of one or two models, and a non-automatic, more taxing level of model construction.

The aim of the present article is to advance the understanding of this intuitive and elementary level of reasoning presupposed by both theories.

Although psychological theories tend to present deduction as an all-or none process even at its elementary stage deduction is a complex phenomenon with several aspects. One prominent aspect is the deduction sequence itself, that is, the passage from one step to another during the search for a conclusion from a set of premises. A second aspect is meta-deductive: it consists in the ability to keep track of the unfolding of a deductive reasoning, by locating how single steps relate to the overall structure of a reasoning process. A third aspect is the ability to temporarily store the representations needed to either produce a deduction sequence or to supervise the structure of a deduction sequence. Potentially, deficits to any one of the three components may produce reasoning impairments.

Because the main aim of a theory of reasoning is to predict how subjects will respond to deductive problems, naturally most reasoning research has focused on the deduction process rather than on the other components. For deduction, mental logic holds that the complexity of a (elementary) problem is a function of the length of the proof needed to evaluate or generate the conclusion weighted by the individual difficulties of the rules entering the proof. By contrast, for the mental model theory the difficulty of a problem is a function of the number of models required to validate a putative conclusion. To explore the predictions of both theories, the percentage of correct solutions to deductive problems is a rough but fundamental index. Several studies show that length of proof is a good predictor of participants’ errors (Braine, 1998, Braine et al., 1984, Braine et al., 1995; Braine & O’Brien, 1998a; Lea, 1995, Lea et al., 1990; Yang, Braine, & O’Brien, 1998). Other studies suggest that also the number of models correlates with errors (Johnson-Laird & Bara, 1984; Johnson-Laird, Legrenzi, Girotto, Legrenzi, & Caverni, 1999; Johnson-Laird, Byrne, & Schaeken, 1992; Schaeken, Johnson-Laird, & d’Ydewalle, 1996). Such studies assume that models can be unambiguously counted, which may not be the case (Bonatti, 1994, Bonatti, 1998).

Sensitivity to proof structure, although fundamental has received less attention, and almost exclusively within the framework of the mental logic theory. This interest is easily understood. A deductive proof is a structured object, often requiring several intermediate subgoals. To reach a conclusion, a reasoner must apply individual rules, but also maintain a general sense of their position within the reasoning process, and/or a conception of the distance between the premises and the conclusion, over and above each single step involved in the proof. By monitoring the structure of the reasoning process, s/he can better judge the distance between current state and the final goal, and thus allocate resources that are needed to solve the problem. A failure to do this may lead to errors. For example, in solving a problem a reasoner may be led to explore the consequences of a supposition, perhaps before finally discarding it. However, if s/he does not monitor the overall reasoning process, s/he may think s/he has reached a final conclusion about the consequences while in fact s/he is still within an intermediate step of proof construction, one in which the current intermediate conclusion is valid only under that supposition. This insensitivity of the structure of a proof will lead the reasoner to make errors. Evidence exists that participants are sensitive to the suppositional structure of a mental proof (Marcus & Rips, 1979).

Sensitivity to overall problem structure has been mostly studied by probing the difficulty judgments of the participants for elementary deductive problems. Studies have shown that participants can form stable and well differentiated difficulty judgments, even for elementary reasoning problems (e.g., Braine et al., 1984), and that they correlate with different degrees of proof complexity.1

In complementary fashion, the role of memory in deduction has been studied especially within the mental model frameworks. Again, the reason for this interest can be easily understood. As models are memory structures, a natural prediction of mental models is that limited working memory will reduce reasoning abilities. This prediction has been explored with varying degree of success by studying developmental differences in reasoning abilities, or by using tasks varying concurrent memory load (Copeland & Radvansky, 2004; De Neys et al., 2005a, De Neys et al., 2005b; Markovits, Doyon, & Simoneau, 2002).

In short, all three dimensions of elementary deductive reasoning have been recognized and studied in the psychological literature, although not within the unified frame which we propose. Clearly, an approach that could assess the respective role of these factors would be highly informative for theories of deduction. For this purpose, studies on the involvement of the frontal cortex in elementary reasoning can be extremely useful.

We have argued that, in order to carry out elementary deductions, first, rules for deriving inferences (or procedures to construct models) must be recruited; then, the ability to represent the overall unfolding of the proof is required, and finally, memory is needed in order to represent the premises, the intermediate states of a derivation, and its overall structure. In all these functions, the frontal cortex may play a crucial role. Several lines of evidence suggest that the subprocesses we postulate in elementary reasoning involve specific frontal regions. Firstly, in general, the frontal cortex seems to be involved during the execution of deductive tasks, more specifically the left lateral and medial cortex (Fangmeier, Knauff, Ruff, & Sloutsky, 2006; Goel, Buchel, Frith, & Dolan, 2000; Goel & Dolan, 2003; Monti, Osherson, Martinez, & Parsons, 2007; Reverberi et al., submitted for publication, Reverberi et al., 2007; but see also Reverberi, Rusconi, Paulesu, & Cherubini, 2009). Secondly the fronto-polar cortex (mainly, Brodmann Area 10) has been linked to “cognitive branching” or “multiple sub-goal scheduling”, i.e. the human ability to hold in mind goals while exploring and processing secondary goals (Braver & Bongiolatti, 2002; Burgess, Veitch, de Lacy Costello, & Shallice, 2000; Koechlin, Basso, Pietrini, Panzer, & Grafman, 1999; Ramnani & Owen, 2004). As we recalled, this ability is important in order to build and manipulate the overall logical structure of a deductive problem. Finally, the dorsolateral frontal cortex is known to be involved in verbal working memory (Baddeley, 2003; D’Esposito & Postle, 1999; Owen, McMillan, Laird, & Bullmore, 2005). These abilities are all also required to carry out elementary deductions.

However, limited neuropsychological evidence is available about the role of frontal cortex in deduction. In particular, to our knowledge, its role in elementary deduction has not been directly corroborated by any neuropsychological study. Two neuropsychological group studies are available to date specifically aimed at investigating the role of the frontal cortex in propositional deductive reasoning (Goel, Shuren, Sheesley, & Grafman, 2004; Adolphs, Tranel, Bechara, Damasio, & Damasio, 1996). Such studies are unlikely to shed light on elementary reasoning, as they explore the neural basis of the Wason selection task (Wason, 1968). Although prominent in the psychological literature about reasoning, it is now widely agreed that despite its deceptively simple propositional-like form the Wason selection task taps onto several different inferential mechanisms (Girotto, Kemmelmeier, Sperber, & Jean-Baptiste, 2001; Sperber, Cara, & Girotto, 1995; Cosmides, 1989). As a consequence, it becomes very difficult to interpret neuropsychological results based on the Wason selection task.

The aim of our study is to provide novel evidence specifically addressing the role of frontal cortex in elementary propositional deduction and, if possible, to clarify the neurological basis of the functional distinction between the different dimensions of the deduction process we discussed.

Section snippets

Participants

Thirty-six Italian patients with a single focal brain lesion as determined by a CT or an MRI scan were recruited from the Neurological and Neurosurgical wards of the Ospedale Civile in Udine (Italy). All patients gave their consent to participate to the study, which was approved by the ethical committee of SISSA-ISAS (Scuola Internazionale Superiore di Studi Avanzati - International School for Advanced Studies). The etiology of the patient sample was mixed: stroke, neoplasm and arachnoid cyst (

Effect of demographic factors, time since lesion, lesion size and etiology

We evaluated the effect of demographic factors, time since lesion and etiology on the accuracy score of the deduction test. Both age and education significantly affected the proportion of correct responses in the patient group (age: R2 = 0.232, F(1,34) = 10.274, p = 0.003; education: R2 = 0.232, F(1,34) = 10.270, p = 0.003). None of these factors were significant in the control group. We also ran a regression analysis with the logarithm of the days from onset of the disease (Table 2) as the independent

Discussion

Elementary deduction is the ability to draw conclusions without reflection from explicit or implicit premises, on the basis of their logical forms. This ability is involved in many aspects of human cognition, such as belief fixation, conversational exchanges, and internal thinking processes. Clarifying its nature and its neural basis is an important task, which researchers only began to approach recently.

The present study had two main objectives. The first was to provide neuropsychological

Conclusions

The present study explored the contribution of specific regions of the human frontal cortex to elementary deduction. We explored the view that even elementary reasoning involves multiple functional components, with possibly different localizations.

We found that left lateral and medial frontal cortices have a critical role in elementary deduction, whereas, lesions to right lateral cortex did not affect deductive competence. Furthermore, by also evaluating working memory span and meta-deductive

Acknowledgments

C.R. and L.L.B. conceived the research and wrote the paper. C.R. carried out all the experiments and analyzed the data. T.S. supervised the research, read and commented all the versions of the manuscript. The patients were under the care of M.S. who also provided the clinical assessments. SDA classified patients in the lesion groups and drew lesions on the standard brain. We thank two anonymous reviewers for insightful comments on a first version of the paper.

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