Recent studies have shown that deductive reasoning skills are related to mathematical abilities. Nevertheless, so far the links between mathematical abilities and these two forms of deductive inference have not been investigated in a single study. It is also unclear whether these inference forms are related to both basic maths skills and mathematical reasoning, and whether these relationships still hold if the effects of fluid intelligence are controlled. We conducted a study with 87 adult participants. The results showed that transitive (...) reasoning skills were related to performance on a number line task, and conditional inferences were related to arithmetic skills. Additionally, both types of deductive inference were related to mathematical reasoning skills, although transitive and conditional reasoning ability were unrelated. Our results also highlighted the important role that ordering abilities play in mathematical reasoning, extending findings regarding the role of ordering abilities in basic maths skills. These results have implications for the theories of mathematical and deductive reasoning, and they could inspire the development of novel educational interventions. (shrink)

Cognitive scientists have revealed systematic errors in human reasoning. There is disagreement about what these errors indicate about human rationality, but one upshot seems clear: human reasoning does not seem to fit traditional views of human rationality. This concern about rationality has made its way through various fields and has recently caught the attention of philosophers. The concern is that if philosophers are prone to systematic errors in reasoning, then the integrity of philosophy would be threatened. In this paper, I (...) present some of the more famous work in cognitive science that has marshaled this concern. Then I present reasons to think that those with training in philosophy will be less prone to certain systematic errors in reasoning. The suggestion is that if philosophers could be shown to be less prone to such errors, then the worries about the integrity of philosophy could be constrained. Then I present evidence that, according to performance on the CRT (Frederick 2005), those who have benefited from training and selection in philosophy are indeed less prone to one kind of systematic error: irrationally arbitrating between intuitive and reflective responses. Nonetheless, philosophers are not entirely immune to this systematic error, and their proclivity for this error is statistically related to their responses to a variety of philosophical questions. So, while the evidence herein puts constraints on the worries about the integrity of philosophy, it by no means eliminates these worries. The conclusion, then, is that the present evidence offers prima facie reasons to ascribe a mitigated privilege to philosophers' ability to rationally arbitrate between intuitive and reflective responses. (shrink)

A novel explanation of belief bias in relational reasoning is presented based on the role of working memory and retrieval in deductive reasoning, and the influence of prior knowledge on this process. It is proposed that belief bias is caused by the believability of a conclusion in working memory which influences its activation level, determining its likelihood of retrieval and therefore its effect on the reasoning process. This theory explores two main influences of belief on the activation levels of these (...) conclusions. First, believable conclusions have higher activation levels and so are more likely to be recalled during the evaluation of reasoning problems than unbelievable conclusions, and therefore, they have a greater influence on the reasoning process. Secondly, prior beliefs about the conclusion have a base level of activation and may be retrieved when logically irrelevant, influencing the evaluation of the problem. The theory of activation and memory is derived from the Atomic Components of Thought-Rational (ACT-R) cognitive architecture and so this account is formalized in an ACT-R cognitive model. Two experiments were conducted to test predictions of this model. Experiment 1 tested strength of belief and Experiment 2 tested the impact of a concurrent working memory load. Both of these manipulations increased the main effect of belief overall and in particular raised belief-based responding in indeterminately invalid problems. These effects support the idea that the activation level of conclusions formed during reasoning influences belief bias. This theory adds to current explanations of belief bias by providing a detailed specification of the role of working memory and how it is influenced by prior knowledge. (shrink)

When the absence of an event causes some outcome, it is an instance of omissive causation. For instance, not eating lunch may cause you to be hungry. Recent psychological proposals concur that the mind represents causal relations, including omissive causal relations, through mental simulation, but they disagree on the form of that simulation. One theory states that people represent omissive causes as force vectors; another states that omissions are representations of contrasting counterfactual simulations; a third argues that people think about (...) omissions by representing sets of iconic possibilities – mental models – in a piecemeal fashion. In this paper, we tease apart the empirical predictions of the three theories and describe experiments that run counter to two of them. Experiments 1 and 2 show that reasoners can infer temporal relations from omissive causes – a pattern that contravenes the force theory. Experiment 3 asked participants to list the possibilities consistent with an omissive cause – it found that they tended to list particular privileged possibilities first, most often, and faster than alternative possibilities. The pattern is consistent with the model theory, but inconsistent with the contrast hypothesis. We marshal the evidence and explain why it helps to solve a long-standing debate about how the mind represents omissions. (shrink)

(2013). The processes of inference. Argument & Computation: Vol. 4, Formal Models of Reasoning in Cognitive Psychology, pp. 4-20. doi: 10.1080/19462166.2012.674060.

Over the last quarter century, the dominant tendency in comparative cognitive psychology has been to emphasize the similarities between human and nonhuman minds and to downplay the differences as (Darwin 1871). In the present target article, we argue that Darwin was mistaken: the profound biological continuity between human and nonhuman animals masks an equally profound discontinuity between human and nonhuman minds. To wit, there is a significant discontinuity in the degree to which human and nonhuman animals are able to approximate (...) the higher-order, systematic, relational capabilities of a physical symbol system (PSS) (Newell 1980). We show that this symbolic-relational discontinuity pervades nearly every domain of cognition and runs much deeper than even the spectacular scaffolding provided by language or culture alone can explain. We propose a representational-level specification as to where human and nonhuman animals' abilities to approximate a PSS are similar and where they differ. We conclude by suggesting that recent symbolic-connectionist models of cognition shed new light on the mechanisms that underlie the gap between human and nonhuman minds. (shrink)

No present theory explains the inferences people draw about the real world when reasoning about “bouletic” relations, that is, predicates that express desires, such aswantin “Lee wants to be in love”. Linguistic accounts ofwantdefine it in terms of a relation to a desirer's beliefs, and how its complement is deemed desirable. In contrast, we describe a new model‐based theory that posits that by default, desire predicates such aswantcontrast desires against facts. In particular,A wants Pimplies by default thatPis not the case, (...) because you cannot want what is already true. On further deliberation, reasoners may infer thatA believes, but does not know for certain, thatPis not the case. The theory makes several empirical predictions about how people interpret, assess the consistency of, and draw conclusions from desire predicates likewant. Seven experiments tested and validated the theory's central predictions. We assess the theory in light of recent proposals of desire predicates. (shrink)

Spearman’s Law of Diminishing Returns holds that correlation between general /fluid intelligence factor and other cognitive abilities weakens with increasing ability level. Thus, cognitive processing in low ability people is most strongly saturated by g/gf, whereas processing in high ability people depends less on g/gf. Numerous studies demonstrated that low g is more strongly correlated with crystallized intelligence/creativity/processing speed than is high g, however no study tested an analogous effect in the case of working memory. Our aim was to investigate (...) SLODR for the relationship between Gf and WM capacity, using a large data set from our own previous studies. We tested alternative regression models separately for three types of WM tasks that tapped short-term memory storage, attention control, and relational integration, respectively. No significant SLODR effect was found for any of these tasks. Each task shared with Gf virtually the same amount of variance in the case of low- and high-ability people. This result suggests that Gf and WM rely on one and the same cognitive mechanism. (shrink)

Euclidean diagrammatic reasoning refers to the diagrammatic inferential practice that originated in the geometrical proofs of Euclid’s Elements. A seminal philosophical analysis of this practice by Manders (‘The Euclidean diagram’, 2008) has revealed that a systematic method of reasoning underlies the use of diagrams in Euclid’s proofs, leading in turn to a logical analysis aiming to capture this method formally via proof systems. The central premise of this paper is that our understanding of Euclidean diagrammatic reasoning can be fruitfully advanced (...) by confronting these logical and philosophical analyses with the field of cognitive science. Surprisingly, central aspects of the philosophical and logical analyses resonate in very natural ways with research topics in mathematical cognition, spatial cognition and the psychology of reasoning. The paper develops these connections, concentrating on four issues: (1) the cognitive origins of Euclidean diagrammatic reasoning, (2) the cognitive representations of spatial relations in Euclidean diagrams, (3) the nature of the cognitive processes and cognitive representations involved in Euclidean diagrammatic reasoning seen as a form of visuospatial relational reasoning and (4) the complexity of Euclidean diagrammatic reasoning for the human cognitive system. For each of these issues, our analysis generates concrete experiment proposals, opening thereby the way for further empirical investigations. The paper is thus a prolegomenon to a research program on Euclidean diagrammatic reasoning at the crossroads of logic, philosophy and cognitive science. (shrink)

This paper offers a modeling account of episodic representation. I argue that the episodic system constructsmental models: representations that preserve the spatiotemporal structure of represented domains. In prototypical cases, these domains are events: occurrences taken by subjects to have characteristic structures, dynamics and relatively determinate beginnings and ends. Due to their simplicity and manipulability, mental event models can be used in a variety of cognitive contexts: in remembering the personal past, but also in future-oriented and counterfactual imagination. As structural representations, (...) they allow surrogative reasoning, supporting inferences about their constituents which can be used in reasoning about the represented events. (shrink)

We describe a novel computational theory of how individuals segment perceptual information into representations of events. The theory is inspired by recent findings in the cognitive science and cognitive neuroscience of event segmentation. In line with recent theories, it holds that online event segmentation is automatic, and that event segmentation yields mental simulations of events. But it posits two novel principles as well: first, discrete episodic markers track perceptual and conceptual changes, and can be retrieved to construct event models. Second, (...) the process of retrieving and reconstructing those episodic markers is constrained and prioritized. We describe a computational implementation of the theory, as well as a robotic extension of the theory that demonstrates the processes of online event segmentation and event model construction. The theory is the first unified computational account of event segmentation and temporal inference. We conclude by demonstrating now neuroimaging data can constrain and inspire the construction of process-level theories of human reasoning. (shrink)

The aim of this article is to strengthen links between cognitive brain research and formal logic. The work covers three fundamental sorts of logical inferences: reasoning in the propositional calculus, i.e. inferences with the conditional “if...then”, reasoning in the predicate calculus, i.e. inferences based on quantifiers such as “all”, “some”, “none”, and reasoning with n-place relations. Studies with brain-damaged patients and neuroimaging experiments indicate that such logical inferences are implemented in overlapping but different bilateral cortical networks, including parts of the (...) fronto-temporal cortex, the posterior parietal cortex, and the visual cortices. I argue that these findings show that we do not use a single deterministic strategy for solving logical reasoning problems. This account resolves many disputes about how humans reason logically and why we sometimes deviate from the norms of formal logic. (shrink)

The commentators of our target article present several detailed arguments to refute the opposing theory. The real issue, however, seems to be the fundamental question of how the mind represents the content of beliefs. We distinguish between qualitative, quantitative and comparative approaches to modeling uncertain beliefs. We describe which theory falls into which of these classes. We also argue that the comparative level is the most fundamental, and challenge commentators to justify why they think that beliefs have more or less (...) structure in the human mind than can be captured at the comparative level. (shrink)

This article presents a fundamental advance in the theory of mental models as an explanation of reasoning about facts, possibilities, and probabilities. It postulates that the meanings of compound assertions, such as conditionals (if) and disjunctions (or), unlike those in logic, refer to conjunctions of epistemic possibilities that hold in default of information to the contrary. Various factors such as general knowledge can modulate these interpretations. New information can always override sentential inferences; that is, reasoning in daily life is defeasible (...) (or nonmonotonic). The theory is a dual process one: It distinguishes between intuitive inferences (based on system 1) and deliberative inferences (based on system 2). The article describes a computer implementation of the theory, including its two systems of reasoning, and it shows how the program simulates crucial predictions that evidence corroborates. It concludes with a discussion of how the theory contrasts with those based on logic or on probabilities. (shrink)

Relational reasoning is a complex form of human cognition involving the evaluation of relations between mental representations of information. Prior studies have modified stimulus properties of relational reasoning problems and examined differences in difficulty between different problem types. While subsets of these stimulus properties have been addressed in separate studies, there has not been a comprehensive study, to our knowledge, which investigates all of these properties in the same set of stimuli. This investigative gap has resulted in different findings across (...) studies which vary in task design, making it challenging to determine what stimulus properties make relational reasoning—and the putative formation of mental models underlying reasoning—difficult. In this article, we present the Multidimensional Relational Reasoning Task, a task which systematically varied an array of stimulus properties within a single set of relational reasoning problems. Using a mixed-effects framework, we demonstrate that reasoning problems containing a greater number of the premises as well as multidimensional relations led to greater task difficulty. The MRRT has been made publicly available for use in future research, along with normative data regarding the relative difficulty of each problem. (shrink)

The neural basis of developmental changes in transitive reasoning in parietal regions was examined, using voxel-based morphometry. Young adolescents and adults performed a transitive reasoning task, subsequent to undergoing anatomical magnetic resonance imaging brain scans. Behaviorally, adults reasoned more accurately than did the young adolescents. Neural results showed less grey matter density in superior parietal cortex in the adults than in the young adolescents, possibly due to a developmental period of synaptic pruning; improved performance in the reasoning task was negatively (...) correlated with grey matter density in superior parietal cortex in the adolescents, but not in the adult group; and the latter results were driven by the more difficult trials, requiring greater spatial manipulation. Taken together, the results support the idea that during development, regions in superior parietal cortex are fine-tuned, to support more robust spatial manipulation, resulting in gre... (shrink)

The theory of mental models postulates that meaning and knowledge can modulate the interpretation of conditionals. The theory's computer implementation implied that certain conditionals should be true or false without the need for evidence. Three experiments corroborated this prediction. In Experiment 1, nearly 500 participants evaluated 24 conditionals as true or false, and they justified their judgments by completing sentences of the form, It is impossible that A and ___ appropriately. In Experiment 2, participants evaluated 16 conditionals and provided their (...) own justifications, which tended to be explanations rather than logical justifications. In Experiment 3, the participants also evaluated as possible or impossible each of the four cases in the partitions of 16 conditionals: A and C, A and not-C, not-A and C, not-A and not-C. These evaluations corroborated the model theory. We consider the implications of these results for theories of reasoning based on logic, probabilistic logic, and suppositions. (shrink)

We examine schoolchildren’s reasoning with spatial relations, such as ‘is to the left of’. Our aims are to obtain a more precise account of the effect of working memory on reasoning, a more detaile...

In the ongoing research of the functions of consciousness, special emphasis has been put on integration of information: the ability to combine different signals into a coherent, unified one. Several theories of consciousness hold that this ability depends on – or at least goes hand in hand with – conscious processing. Yet some empirical findings have suggested otherwise, claiming that integration of information could take place even without awareness. Trying to reconcile this apparent contradiction, the “windows of integration” hypothesis claims (...) that conscious access enables signal processing over large integration windows. The hypothesis applies to integration windows defined either temporally, spatially, or semantically. In this review, we explain the hypothesis and re-examine it in light of new studies published since it was suggested. In line with the hypothesis, these studies provide compelling evidence for unconscious integration, but also demonstrate its limits with respect to time, space, and semantic distance. The review further highlights open questions that still need to be pursued to demonstrate the applicability of the WOI hypothesis as a guiding principle for understanding the depth and scope of unconscious processes. (shrink)

This thesis investigates the relationship between eye movements, mental imagery and memory retrieval in four studies based on eye-tracking experiments. The first study is an investigation of eye movements during mental imagery elicited both visually and verbally. The use of complex stimuli and the development of a novel method where eye movements are recorded concurrently with verbal data enabled the above-mentioned relationship to be studied to an extent going beyond what previous research had been able to do. Eye movements were (...) found to closely reflect content and spatial layout while participants were listening to a spoken scene description, while they were describing the same scene from memory, and while they were describing a picture they had previously seen. This effect was equally strong during recall from memory irrespective of whether the scene visualised had originally been inspected visually by the participants or whether it was constructed whole-cloth from long-term memory. It was also found that eye movements "to nothing" appeared both when the participants were visualising scenes while looking at a blank screen and when they were doing so in complete darkness. The second study explored an effect frequently observed in the first study, involving a "scaling-down" during recall of participants' gaze patterns to an area smaller than that occupied by the stimulus encoded. It was found that this scaling effect correlated with spatial-imagery ability: the gaze patterns of participants with weaker spatial-imagery ability were closer in size to the encoded scene than the gaze patterns of those stronger in spatial-imagery ability. In the third study, the role of eye movements during mental imagery was investigated in four experiments where eye movements were prohibited during either the encoding phase or the recall phase. Experiments 1 and 2 showed that maintaining central fixation during visual or auditory encoding, respectively, had no effect on how eye movements were executed during recall. Thus, oculomotor events during recall are not reproductions of those produced during encoding. In Experiments 3 and 4, central fixation was instead maintained during recall. This turned out to alter and impair scene recollection, irrespective of the modality of encoding. Finally, in the fourth study, the functional role of eye movements in relation to memory retrieval was further investigated by means of direct eye-movement manipulation in the retrieval phase of an episodic-memory task. Four conditions were used: free viewing on a blank screen, maintaining central fixation, viewing within a square congruent with the location of the objects to be recalled, and viewing within a square incongruent with the location of the objects to be recalled. The results obtained show that gaze position plays an active and facilitatory role during memory retrieval. The findings from these studies are discussed in the light of current theories regarding eye movements during mental imagery and memory retrieval. (shrink)

The present contribution argues that transitive reasoning, as exemplified in paradigms of linear order construction in mental space, is associated with spatial effects. Starting from robust findings from the early 70s, research so far has widely discussed the symbolic distance effect. This effect shows that after studying pairs of relations, e.g., “A > B,” “B > C,” and “D > E,” participants are more correct, and faster in correct responding, the wider the “distance” between two elements within the chain A (...) > B > C > D > E. The SDE has often been given spatial interpretations, but alternatively, non-spatial models of the effect are also viable on the empirical basis so far, which means the question about spatial contributions to the construction of analog representations of rank orders is still open. We suggest here that laterality effects can add the necessary additional information to support the idea of spatial processes. We introduce anchoring effects in terms of showing response advantages for congruent versus incongruent pairings of presentation location on a screen on the one hand, and the hypothetical spatial arrangement of the order in mental space, on the other hand. We report pertinent findings and discuss anchoring paradigms with respect to their internal validity as well as their being rooted in basic mechanisms of trained reading/writing direction. (shrink)

Semantic studies on diagrammatic notations (Barwise & Etchemendy, ; Shimojima, ; Stenning & Lemon, ) have revealed that the “non-deductive,” “emergent,” or “perceptual” effects of diagrams (Chandrasekaran, Kurup, Banerjee, Josephson, & Winkler, ; Kulpa, ; Larkin & Simon, ; Lindsay, ) are all rooted in the exploitation of spatial constraints on graphical structures. Thus, theoretically, this process is a key factor in inference with diagrams, explaining the frequently observed reduction of inferential load. The purpose of this study was to examine (...) the empirical basis for this theoretical suggestion, focusing on the reality of the constraint-exploitation strategy in actual practices of diagrammatic reasoning. Eye movements were recorded while participants used simple position diagrams to solve three- or four-term transitive inference problems. Our experiments revealed that the participants could exploit spatial constraints on graphical structures even when (a) they were not in the position of actually manipulating diagrams, (b) the semantic rule for the provided diagrams did not match their preferences, and (c) the constraint-exploitation strategy invited a partly adverse effect. These findings indicate that the hypothesized process is in fact robust, with the potential to broadly account for the inferential advantage of diagrams. (shrink)