Cognitive and AI models of reasoning

Although relatively few in number, cognitive neuroscience studies of reasoning have two general implications for cognitive theories of deduction. First, an important distinction among these theories is whether they focus on the effect of personally relevant content on the processes and representations underlying deductive reasoning. Evidence is reviewed indicating that there is a neuroanatomical basis for both content-independent and content-dependent theories of deduction. Clinical and neuroimaging studies appear to show that content-independent reasoning is mediated by the left hemisphere, whereas content-dependent reasoning is mediated by regions in the right hemisphere and the bilateral ventromedial frontal cortex. In normal subjects, reasoning is likely to be based on contributions from both hemispheres. Second, clinical evidence indicates that the visuospatial processes used in deductive reasoning are mediated by the posterior areas of the left hemisphere, and that verbal and visuospatial reasoning representations overlap at the neuroanatomical level. This finding weighs against the claims of mental-model theory that deduction involves a significant nonverbal component. Further investigation, particularly with contemporary neuroimaging methods, is needed to test these preliminary conclusions.     

归纳推理和演绎推理的关系理论及其模型

推理是人类高级认知过程的一种,相关的心理学研究一般将其分为归纳推理和演绎推理两个方面。归纳推理是从特殊到一般的推理过程,与之相对的演绎推理则是从一般到特殊的过程。归纳推理和演绎推理的关系问题是当前心理推理研究领域的一个重点问题。这一问题主要有两种理论解释：一种是单过程理论,该理论认为归纳推理和演绎推理本质上是同一个认知过程,以单过程理论为基础构建的推理模型称为单维模型;另一种是双过程理论,认为归纳推理和演绎推理是两个不同的认知过程,并不同程度地受到启发和分析过程的影响。未来研究可多关注推理的时间进程,以及采用不同的研究方法对各自理论提供数据支持。     

Model theory of deduction: a unified computational approach

One of the most debated questions in psychology and cognitive science is the nature and the functioning of the mental processes involved in deductive reasoning. However, all existing theories refer to a specific deductive domain, like syllogistic, propositional or relational reasoning.
Our goal is to unify the main types of deductive reasoning into a single set of basic procedures. In particular, we bring together the microtheories developed from a mental models perspective in a single theory, for which we provide a formal foundation. We validate the theory through a computational model (UNICORE) which allows fine-grained predictions of subjects' performance in different reasoning domains.
The performance of the model is tested against the performance of experimental subjects—as reported in the relevant literature—in the three areas of syllogistic, relational and propositional reasoning. The computational model proves to be a satisfactory artificial subject, reproducing both correct and erroneous performance of the human subjects. Moreover, we introduce a developmental trend in the program, in order to simulate the performance of subjects of different ages, ranging from children (3–6) to adolescents (8–12) to adults (>21). The simulation model performs similarly to the subjects of different ages.
Our conclusion is that the validity of the mental model approach is confirmed for the deductive reasoning domain, and that it is possible to devise a unique mechanism able to deal with the specific subareas. The proposed computational model (UNICORE) represents such a unifying structure.     

Multiple explanations for multiply quantified sentences: are multiple models necessary?

Johnson-Laird, Byrne, and Tabossi (1989) presented a theory of deductive reasoning for inference problems using multiply quantified premises (e.g., "All of the squares are connected to some of the circles"). Their theory classifies such problems into those that require subjects to construct only 1 mental model and those that require multiple models. They presented data that corroborate the theory. This article shows that Johnson-Laird et al.'s major results can be explained without invoking mental models or, in fact, deductive reasoning at all. Furthermore, it is demonstrated that, contrary to the assumption of these authors, reversing the order of the quantifiers in a multiply quantified sentence may produce a sentence that is both more difficult to comprehend and more ambiguous. Finally, some implications for theories of how people understand multiply quantified sentences are noted.     

Reconnecting interpretation to reasoning through individual differences

Computational theories of mind assume that participants interpret information and then reason from those interpretations. Research on interpretation in deductive reasoning has claimed to show that subjects' interpretation of single syllogistic premises in an “immediate inference” task is radically different from their interpretation of pairs of the same premises in syllogistic reasoning tasks (Newstead, 1989, 1995; Roberts, Newstead, & Griggs, 2001). Narrow appeal to particular Gricean implicatures in this work fails to bridge the gap. Grice's theory taken as a broad framework for credulous discourse processing in which participants construct speakers' “intended models” of discourses can reconcile these results, purchasing continuity of interpretation through variety of logical treatments. We present exploratory experimental data on immediate inference and subsequent syllogistic reasoning. Systematic patterns of interpretation driven by two factors (whether the subject's model of the discourse is credulous, and their degree of reliance on information packaging) are shown to transcend particular quantifier inferences and to drive systematic differences in subjects' subsequent syllogistic reasoning. We conclude that most participants do not understand deductive tasks as experimenters intend, and just as there is no single logical model of reasoning, so there is no reason to expect a single “fundamental human reasoning mechanism”.     

Reconnecting interpretation to reasoning through individual differences

Computational theories of mind assume that participants interpret information and then reason from those interpretations. Research on interpretation in deductive reasoning has claimed to show that subjects' interpretation of single syllogistic premises in an “immediate inference” task is radically different from their interpretation of pairs of the same premises in syllogistic reasoning tasks (Newstead, 1989, 1995; Roberts, Newstead, & Griggs, 2001). Narrow appeal to particular Gricean implicatures in this work fails to bridge the gap. Grice's theory taken as a broad framework for credulous discourse processing in which participants construct speakers' “intended models” of discourses can reconcile these results, purchasing continuity of interpretation through variety of logical treatments. We present exploratory experimental data on immediate inference and subsequent syllogistic reasoning. Systematic patterns of interpretation driven by two factors (whether the subject's model of the discourse is credulous, and their degree of reliance on information packaging) are shown to transcend particular quantifier inferences and to drive systematic differences in subjects' subsequent syllogistic reasoning. We conclude that most participants do not understand deductive tasks as experimenters intend, and just as there is no single logical model of reasoning, so there is no reason to expect a single “fundamental human reasoning mechanism”.     

Supposition and representation in human reasoning

We report the results of three experiments designed to assess the role of suppositions in human reasoning. Theories of reasoning based on formal rules propose that the ability to make suppositions is central to deductive reasoning. Our first experiment compared two types of problem that could be solved by a suppositional strategy. Our results showed no difference in difficulty between problems requiring affirmative or negative suppositions and very low logical solution rates throughout. Further analysis of the error data showed a pattern of responses, which suggested that participants reason from a superficial representation of the premises in these arguments and this drives their choice of conclusion. Our second experiment employed a different set of suppositional problems but with extremely similar proofs in terms of the rules applied and number of inferential steps required. As predicted by our interpretation of reasoning strategies employed in Experiment 1, logical performance was very much higher on these problems. Our third experiment showed that problems that could be solved by constructing an initial representation of the premises were easier than problems in which this representation was not sufficient. This effect was independent of the suppositional structure of the problems. We discuss the implications of this research for theories of reasoning based on mental models and inference rules.     

The case for a dual-process theory of transitive reasoning

Ever since its popularisation by Piaget around 60 years ago, transitive reasoning (deductively-inferring A > C from premises A > B and B > C) has been of psychological interest both as a mental phenomenon and as a tool in areas of psychological discourse. However, the focus of interest in it has shifted periodically first from child development, to learning disability, to non-humans and currently to cognitive and clinical neuroscience. Crucially, such shifts have always been plagued by one core question – the question of which of two competing paradigms (extensive-training paradigm versus non-training paradigm) is valid for assessing transitive reasoning as originally conceived in Piagetian research. The continued avoidance of this question potentially undermines several important findings recently reported: Such as about exactly what is involved in deducing transitive inferences, which brain regions are critical for reaching transitive inference, and what links exist between weakened deductive transitivity and mental illnesses like schizophrenia. Here, we offer the view that both of the competing paradigms are indexing transitivity, but each one tends to tap a different aspect of it. Then, we summarise studies from child and adult cognitive psychology, disabilities research, and from cognitive neuroscience. These, together with studies of non-human reasoning, seem to afford a theory of transitive reasoning that has two major components; one deductive but the other associative. It is proposed that only a dual-process theory of transitivity (having analytic versus intuitive routes approximate to deductive versus associative processing respectively) can account both for the variety of findings and the apparently-disparate paradigms. However, fuzzy-trace theory (“Gist” processes and representations), if not already embodying such a dual-process theory, will need to be incorporated into any complete theory.     

The logic of social exchange: has natural selection shaped how humans reason? Studies with the Wason selection task

In order to successfully engage in social exchange--cooperation between two or more individuals for mutual benefit--humans must be able to solve a number of complex computational problems, and do so with special efficiency. Following Marr (1982), Cosmides (1985) and Cosmides and Tooby (1989) used evolutionary principles to develop a computational theory of these adaptive problems. Specific hypotheses concerning the structure of the algorithms that govern how humans reason about social exchange were derived from this computational theory. This article presents a series of experiments designed to test these hypotheses, using the Wason selection task, a test of logical reasoning. Part I reports experiments testing social exchange theory against the availability theories of reasoning; Part II reports experiments testing it against Cheng and Holyoak's (1985) permission schema theory. The experimental design included eight critical tests designed to choose between social exchange theory and these other two families of theories; the results of all eight tests support social exchange theory. The hypothesis that the human mind includes cognitive processes specialized for reasoning about social exchange predicts the content effects found in these experiments, and parsimoniously explains those that have already been reported in the literature. The implications of this line of research for a modular view of human reasoning are discussed, as well as the utility of evolutionary biology in the development of computational theories.     

Visual imagery can impede reasoning

Although it is natural to suppose that visual mental imagery is important in human deductive reasoning, the evidence is equivocal. This article argues that reasoning studies have not distinguished between ease of visualization and ease of constructing spatial models. Rating studies show that these factors can be separated. Their results yielded four sorts of relations: (1) visuospatial relations that are easy to envisage visually and spatially, (2) visual relations that are easy to envisage visually but hard to envisage spatially, (3) spatial relations that are hard to envisage visually but easy to envisage spatially, and (4) control relations that are hard to envisage both visually and spatially. Three experiments showed that visual relations slow down the process of reasoning in comparison with control relations, whereas visuospatial and spatial relations yield inferences comparable with those of control relations. We conclude that irrelevant visual detail can be a nuisance in reasoning and can impede the process.     

Syntactic principles of heuristic-driven theory projection

Analogy making is a central construct in human cognition and plays an important role to explain cognitive abilities. While various psychologically or neurally inspired theories for analogical reasoning have been proposed, there is a lack of a logical foundation for analogical reasoning in artificial intelligence and cognitive science. We aim to close this gap and propose heuristic-driven theory projection (HDTP), a mathematically sound framework for analogy making. HDTP represents knowledge about the source and the target domain as first-order logic theories and compares them for structural commonalities using anti-unification. The paper provides an overview of the syntactic principles of HDTP, explains all phases of analogy making at a formal level, and illustrates these phases with examples.     

Explaining modulation of reasoning by belief

Although deductive reasoning is a closed system, one's beliefs about the world can influence validity judgements. To understand the associated functional neuroanatomy of this belief-bias we studied 14 volunteers using event-related fMRI, as they performed reasoning tasks under neutral, facilitatory and inhibitory belief conditions. We found evidence for the engagement of a left temporal lobe system during belief-based reasoning and a bilateral parietal lobe system during belief-neutral reasoning. Activation of right lateral prefrontal cortex was evident when subjects inhibited a prepotent response associated with belief-bias and correctly completed a logical task, a finding consistent with its putative role in cognitive monitoring. By contrast, when logical reasoning was overcome by belief-bias, there was engagement of ventral medial prefrontal cortex, a region implicated in affective processing. This latter involvement suggests that belief-bias effects in reasoning may be mediated through an influence of emotional processes on reasoning.     

Deductive Reasoning in the Structuralist Approach

The distinction between the syntactic and the semantic approach to scientific theories emerged in formal philosophy of science. The semantic approach is commonly considered more advanced and more successful than the syntactic one, but the transition from the one approach to the other was not brought about without any loss. In essence, it is the formal analysis of atomic propositions and the analysis of deductive reasoning that dropped out of consideration in at least some of the elaborated versions of the semantic approach. In structuralist theory of science, as founded by Sneed and Stegmüller, the focus is on global propositions concerning the question of whether or not certain empirical systems satisfy a set-theoretic predicate that encodes the axioms of a scientific theory. Hence, an analysis of deductive reasoning from atomic premisses with the help of a given theory is missing. The objective of the present paper is to develop a deductive system on the basis of the structuralist framework. This system comes with a novel formulation of empirical propositions in structuralism.     

The relation between young children's cognitive role-taking and mothers' preference for a conflict-inducing childrearing method

In this study, we examined children's cognitive role-taking in relation to their mothers' choices of techniques to solve domestic dilemmas involving children's misbehavior, social skills, and logical reasoning. Results showed that a mother's preference for the childrearing strategy known as distancing, which uses a Socratic or dialectical inquiry to create cognitive conflict in the child, bore a significant association to her child's advancement in cognitive role-taking skill. This finding is discussed in relation to theories of cognitive development that postulate that mental conflict or tension stimulates cognitive growth. Practical factors that might inhibit mothers from making effective use of the distancing technique are also considered.     

Are there Reasons to Challenge a Symbolic Computationalist Approach in Explaining Deductive Reasoning?

The majority of the existing theories explaining deductive reasoning could be included in a classic computationalist approach of the cognitive processes. In fact, deductive reasoning could be seen to be the pinnacle of the symbolic computationalism, its last fortress to be defended in the face of new, dynamic, and ecological perspectives over cognition. But are there weak points in that position regarding deductive reasoning? What would be the reasons for which new perspectives could gain in credibility? What could be their most important tenets? The answers given to those questions in the paper include two main points. The first one is that the present empirical data could not sustain unambiguously one view over the other, that they are obtained in artificial experimental conditions, and that there are data that are not easily explainable using the traditional computationalist paradigm. The second one is that approaching the deductive reasoning from dynamic and ecological perspectives could have significant advantages. The most obvious one is the possibility to integrate more easily the research regarding the deductive reasoning with the results obtained in other domains of the psychology (especially in what respects the lower cognitive processes), in artificial intelligence or in neurophysiology. The reasons for that would be that such perspectives, as they are sketched in the paper, would imply, essentially, processes of second-order pattern formation and recognition (as it is the case for perception), embodied cognition, and dynamic processes as the brain ones are.     

Reasoning strategies: the role of working memory and verbal-spatial ability

Evidence increasingly suggests individual differences in strategies adopted on reasoning tasks and that these are either verbal-propositional or visuospatial in nature. However, the cognitive foundations of these strategies remain uncertain. Experiment 1 examined the relationship between the use of working memory resources and strategy selection for syllogistic reasoning. Verbal and spatial strategy users did not differ on working memory capacity, but confirmatory factor analysis indicated that while verbal reasoners draw primarily on verbal working memory, spatial reasoners use both this and spatial resources. Experiment 2 investigated the relationship between strategies and verbal and spatial abilities. Although strategy groups were similar in overall ability, regression analysis showed that performance on a spatial ability measure (Vandenberg mental rotation task) predicted syllogistic reasoning performance, but only for spatial strategy users. The findings provide converging evidence that verbal and spatial strategies are underpinned by related differences in fundamental cognitive factors, drawing differentially on the subcomponents of working memory and on spatial ability.     

Toward a unified theory of human reasoning

This article presents a unified theory of human reasoning. The goal of the theory is to specify what constitutes reasoning, as opposed to other psychological processes, and to characterize the psychological distinction between inductive and deductive reasoning. The theory views reasoning as the controlled and mediated application of three processes— selective encoding, selective comparison, and selective combination—to inferential rules. The first two of these processes are essentially inductive in nature; the third is essentially deductive. The theory describes these three processes, specifies the kinds of inferential rules and their use in several reasoning tasks, and specifies the mediators that affect how well the processes can be applied to the rules. The theory is shown to apply to a variety of reasoning tasks and is compared to other theories as well.     

No interpretation without representation: the role of domain-specific representations and inferences in the Wason selection task

The Wason selection task is a tool used to study reasoning about conditional rules. Performance on this task changes systematically when one varies its content, and these content effects have been used to argue that the human cognitive architecture contains a number of domain-specific representation and inference systems, such as social contract algorithms and hazard management systems. Recently, however, Sperber, Cara & Girotto (Sperber, D., Cara, F., & Girotto, V. (1995). Relevance theory explains the selection task. Cognition, 57, 31-95) have proposed that relevance theory can explain performance on the selection task - including all content effects - without invoking inference systems that are content-specialized. Herein, we show that relevance theory alone cannot explain a variety of content effects - effects that were predicted in advance and are parsimoniously explained by theories that invoke domain-specific algorithms for representing and making inferences about (i) social contracts and (ii) reducing risk in hazardous situations. Moreover, although Sperber et al. (1995) were able to use relevance theory to produce some new content effects in other domains, they conducted no experiments involving social exchanges or precautions, and so were unable to determine which - content-specialized algorithms or relevance effects - dominate reasoning when the two conflict. When experiments, reported herein, are constructed so that the different theories predict divergent outcomes, the results support the predictions of social contract theory and hazard management theory, indicating that these inference systems override content-general relevance factors. The fact that social contract and hazard management algorithms provide better explanations for performance in their respective domains does not mean that the content-general logical procedures posited by relevance theory do not exist, or that relevance effects never occur. It does mean, however, that one needs a principled way of explaining which effects will dominate when a set of inputs activate more than one reasoning system. We propose the principle of pre-emptive specificity - that the human cognitive architecture should be designed so that more specialized inference systems pre-empt more general ones whenever the stimuli centrally fit the input conditions of the more specialized system. This principle follows from evolutionary and computational considerations that are common to both relevance theory and the ecological rationality approach.     

Children's syllogistic reasoning

Most theories of the development of deductive ability propose that children acquire formal rules of inference. An alternative theory assumes that reasoning consists of constructing a mental model of the situation described in the premises, scanning the model for an informative conclusion, and then searching for alternative models that refute this conclusion. Hence, performance should reflect two principal factors: the difficulty of constructing a model, which depends on the “figure” of the premises, and the number of models that have to be evaluated to respond correctly. In Experiment 1, two groups of children (9- to 10- and 11- to 12-year-olds) drew conclusions from 20 pairs of syllogistic premises. The results confirmed that children are affected both by figure and by number of models. Experiment 2 corroborated these findings for all 64 possible forms of syllogistic premises. The development of reasoning ability may therefore depend on the acquisition, not of formal rules of logic, but of procedures for manipulating models.     

The primacy of thinking about possibilities in the development of reasoning

One of the main tenets of the mental model theory is that when individuals reason, they think about possibilities. According to this theory, reasoning on what is possible from the truth of a sentence would be psychologically basic, whereas reasoning the other way round, on the truth or falsity of a sentence from a given state of affairs, would require some meta-ability. The present study tested the developmental corollary of this theory, which is that reasoning about possibilities should develop first, whereas the development of reasoning about truth-value should be delayed. For this purpose, 3rd, 6th, and 9th graders as well as adults were presented with tasks requiring them to evaluate either the possibilities compatible with conditional sentences or the truth-value of these sentences from these same possibilities. The results revealed 2 phenomena. First, the same developmental trend was observed in both tasks with 3 successive interpretational levels: conjunctive, biconditional, and then conditional. Second, there was a developmental lag between the 2 forms of reasoning--with developmental transitions from one level to the next occurring about 3 years later when reasoning about truth-value. The implications of these results for theories of cognitive development and of reasoning are discussed.