Inductive reasoning about causally transmitted properties

Probabilistic causal reasoning under time pressure

While causal reasoning is a core facet of our cognitive abilities, its time-course has not received proper attention. As the duration of reasoning might prove crucial in understanding the underlying cognitive processes, we asked participants in two experiments to make probabilistic causal inferences while manipulating time pressure. We found that participants are less accurate under time pressure, a speed-accuracy-tradeoff, and that they respond more conservatively. Surprisingly, two other persistent reasoning errors-Markov violations and failures to explain away-appeared insensitive to time pressure. These observations seem related to confidence: Conservative inferences were associated with low confidence, whereas Markov violations and failures to explain were not. These findings challenge existing theories that predict an association between time pressure and all causal reasoning errors including conservatism. Our findings suggest that these errors should not be attributed to a single cognitive mechanism and emphasize that causal judgements are the result of multiple processes.

The Bayesian Mutation Sampler Explains Distributions of Causal Judgments

One consistent finding in the causal reasoning literature is that causal judgments are rather variable. In particular, distributions of probabilistic causal judgments tend not to be normal and are often not centered on the normative response. As an explanation for these response distributions, we propose that people engage in 'mutation sampling' when confronted with a causal query and integrate this information with prior information about that query. The Mutation Sampler model (Davis & Rehder, 2020) posits that we approximate probabilities using a sampling process, explaining the average responses of participants on a wide variety of tasks. Careful analysis, however, shows that its predicted response distributions do not match empirical distributions. We develop the Bayesian Mutation Sampler (BMS) which extends the original model by incorporating the use of generic prior distributions. We fit the BMS to experimental data and find that, in addition to average responses, the BMS explains multiple distributional phenomena including the moderate conservatism of the bulk of responses, the lack of extreme responses, and spikes of responses at 50%.

Learning How to Generalize

Generalization is a fundamental problem solved by every cognitive system in essentially every domain. Although it is known that how people generalize varies in complex ways depending on the context or domain, it is an open question how people learn the appropriate way to generalize for a new context. To understand this capability, we cast the problem of learning how to generalize as a problem of learning the appropriate hypothesis space for generalization. We propose a normative mathematical framework for learning how to generalize by learning inductive biases for which properties are relevant for generalization in a domain from the statistical structure of features and concepts observed in that domain. More formally, the framework predicts that an ideal learner should learn to generalize by either taking the weighted average of the results of generalizing according to each hypothesis space, with weights given by how well each hypothesis space fits the previously observed concepts, or by using the most likely hypothesis space. We compare the predictions of this framework to human generalization behavior with three experiments in one perceptual (rectangles) and two conceptual (animals and numbers) domains. Across all three studies we find support for the framework's predictions, including individual-level support for averaging in the third study.

How types of prior knowledge and task properties impact the category-based induction: diverging evidence from the P2, N400, and LPC effects

Category-based induction task was combined with ERP to unravel whether prior knowledge and property interact when inferring on genes or diseases. Larger P2 amplitudes for near taxonomic/causal distances relative to far ones, as well as larger LPC for taxonomic relation relative to thematic relation, are found in both gene and disease tasks. However, smaller N400 is found for taxonomic relation in gene task and thematic relation in disease task, respectively, and larger LPC at 700-850 ms for near taxonomic distance in the gene task and near causal distance in the disease task. These results suggested that the category-based inductive reasoning is context-sensitive, and there may be four stages of category-based inductive reasoning: the early automatic comparison of features/relations (P2), features/relations generalization process (N400), the extraction of common relationship/rule (LPC at 550-700 ms), the inference generation (LPC at 700-850 ms).

Structural thinking about social categories: Evidence from formal explanations, generics, and generalization

Many theories of kind representation suggest that people posit internal, essence-like factors that underlie kind membership and explain properties of category members. Across three studies (N = 281), we document the characteristics of an alternative form of construal according to which the properties of social kinds are seen as products of structural factors: stable, external constraints that obtain due to the kind's social position. Internalist and structural construals are similar in that both support formal explanations (i.e., "category member has property P due to category membership C"), generic claims ("Cs have P"), and the generalization of category properties to individual category members when kind membership and social position are confounded. Our findings thus challenge these phenomena as signatures of internalist thinking. However, once category membership and structural position are unconfounded, different patterns of generalization emerge across internalist and structural construals, as do different judgments concerning category definitions and the dispensability of properties for category membership. We discuss the broader implications of these findings for accounts of formal explanation, generic language, and kind representation.

Perception and conception in understanding evolutionary trees

Relationships depicted in evolutionary trees depend solely on levels of most recent common ancestry. Integrating discipline-based education research in biology with perceptual/cognitive psychology, the authors predicted, however, that the Gestalt principles of perceptual grouping would affect how students interpret these relationships. Experiment 1 (N = 93) found that students segment 6-9 branch trees in accordance with the Gestalt principle of connectedness. Experiment 2 (N = 310) found that students in introductory through advanced biology classes predominantly believed, incorrectly, that the evolutionary relationships among a set of target taxa differed in two trees because the grouping of those taxa differed. Experiment 3 (N = 99) found that students from these same classes were more likely to make inferences consistent with the depicted evolutionary relationships when Gestalt grouping supported those inferences. The authors discuss implications for improving students' understanding of cladograms.

Beyond Markov: Accounting for independence violations in causal reasoning

Although many theories of causal cognition are based on causal graphical models, a key property of such models-the independence relations stipulated by the Markov condition-is routinely violated by human reasoners. This article presents three new accounts of those independence violations, accounts that share the assumption that people's understanding of the correlational structure of data generated from a causal graph differs from that stipulated by causal graphical model framework. To distinguish these models, experiments assessed how people reason with causal graphs that are larger than those tested in previous studies. A traditional common cause network (Y₁←X→Y₂) was extended so that the effects themselves had effects (Z₁←Y₁←X→Y₂→Z₂). A traditional common effect network (Y₁→X←Y₂) was extended so that the causes themselves had causes (Z₁→Y₁→X←Y₂←Z₂). Subjects' inferences were most consistent with the beta-Q model in which consistent states of the world-those in which variables are either mostly all present or mostly all absent-are viewed as more probable than stipulated by the causal graphical model framework. Substantial variability in subjects' inferences was also observed, with the result that substantial minorities of subjects were best fit by one of the other models (the dual prototype or a leaky gate models). The discrepancy between normative and human causal cognition stipulated by these models is foundational in the sense that they locate the error not in people's causal reasoning but rather in their causal representations. As a result, they are applicable to any cognitive theory grounded in causal graphical models, including theories of analogy, learning, explanation, categorization, decision-making, and counterfactual reasoning. Preliminary evidence that independence violations indeed generalize to other judgment types is presented.

Reasoning With Causal Cycles

This article assesses how people reason with categories whose features are related in causal cycles. Whereas models based on causal graphical models (CGMs) have enjoyed success modeling category-based judgments as well as a number of other cognitive phenomena, CGMs are only able to represent causal structures that are acyclic. A number of new formalisms that allow cycles are introduced and evaluated. Dynamic Bayesian networks (DBNs) represent cycles by unfolding them over time. Chain graphs augment CGMs by allowing the presence of undirected links that model feedback relations between variables. Unfolded chain graphs are chain graphs that unfold over time. An existing model of causal cycles (alpha centrality) is also evaluated. Four experiments in which subjects reason about categories with cyclically related features provided evidence against DBNs and alpha centrality and for the two types of chain graphs. Chain graphs-a mechanism for representing the equilibrium distribution of a dynamic system-may thus be good candidates for modeling how people reason causally with complex systems. Applications of chain graphs to areas of cognition other than category-based judgments are discussed.

Going beyond the lesson: Self-generating new factual knowledge in the classroom

For children to build a knowledge base, they must integrate and extend knowledge acquired across separate episodes of new learning. Children's performance was assessed in a task requiring them to self-generate new factual knowledge from the integration of novel facts presented through separate lessons in the classroom. Whether self-generation performance predicted academic outcomes in reading comprehension and mathematics was also examined. The 278 participating children were in kindergarten through Grade 3 (mean age=7.7years, range=5.5-10.3). Children self-generated new factual knowledge through integration in the classroom; age-related increases were observed. Self-generation performance predicted both reading comprehension and mathematics academic outcomes, even when controlling for caregiver education.

Feature saliency and feedback information interactively impact visual category learning

Visual category learning (VCL) involves detecting which features are most relevant for categorization. VCL relies on attentional learning, which enables effectively redirecting attention to object’s features most relevant for categorization, while ‘filtering out’ irrelevant features. When features relevant for categorization are not salient, VCL relies also on perceptual learning, which enables becoming more sensitive to subtle yet important differences between objects. Little is known about how attentional learning and perceptual learning interact when VCL relies on both processes at the same time. Here we tested this interaction. Participants performed VCL tasks in which they learned to categorize novel stimuli by detecting the feature dimension relevant for categorization. Tasks varied both in feature saliency (low-saliency tasks that required perceptual learning vs. high-saliency tasks), and in feedback information (tasks with mid-information, moderately ambiguous feedback that increased attentional load, vs. tasks with high-information non-ambiguous feedback). We found that mid-information and high-information feedback were similarly effective for VCL in high-saliency tasks. This suggests that an increased attentional load, associated with the processing of moderately ambiguous feedback, has little effect on VCL when features are salient. In low-saliency tasks, VCL relied on slower perceptual learning; but when the feedback was highly informative participants were able to ultimately attain the same performance as during the high-saliency VCL tasks. However, VCL was significantly compromised in the low-saliency mid-information feedback task. We suggest that such low-saliency mid-information learning scenarios are characterized by a ‘cognitive loop paradox’ where two interdependent learning processes have to take place simultaneously.

The social Bayesian brain: does mentalizing make a difference when we learn?

When it comes to interpreting others' behaviour, we almost irrepressibly engage in the attribution of mental states (beliefs, emotions…). Such "mentalizing" can become very sophisticated, eventually endowing us with highly adaptive skills such as convincing, teaching or deceiving. Here, sophistication can be captured in terms of the depth of our recursive beliefs, as in "I think that you think that I think…" In this work, we test whether such sophisticated recursive beliefs subtend learning in the context of social interaction. We asked participants to play repeated games against artificial (Bayesian) mentalizing agents, which differ in their sophistication. Critically, we made people believe either that they were playing against each other, or that they were gambling like in a casino. Although both framings are similarly deceiving, participants win against the artificial (sophisticated) mentalizing agents in the social framing of the task, and lose in the non-social framing. Moreover, we find that participants' choice sequences are best explained by sophisticated mentalizing Bayesian learning models only in the social framing. This study is the first demonstration of the added-value of mentalizing on learning in the context of repeated social interactions. Importantly, our results show that we would not be able to decipher intentional behaviour without a priori attributing mental states to others.

A taxonomy of inductive problems

Inductive inferences about objects, features, categories, and relations have been studied for many years, but there are few attempts to chart the range of inductive problems that humans are able to solve. We present a taxonomy of inductive problems that helps to clarify the relationships between familiar inductive problems such as generalization, categorization, and identification, and that introduces new inductive problems for psychological investigation. Our taxonomy is founded on the idea that semantic knowledge is organized into systems of objects, features, categories, and relations, and we attempt to characterize all of the inductive problems that can arise when these systems are partially observed. Recent studies have begun to address some of the new problems in our taxonomy, and future work should aim to develop unified theories of inductive reasoning that explain how people solve all of the problems in the taxonomy.

Causality in thought

Causal knowledge plays a crucial role in human thought, but the nature of causal representation and inference remains a puzzle. Can human causal inference be captured by relations of probabilistic dependency, or does it draw on richer forms of representation? This article explores this question by reviewing research in reasoning, decision making, various forms of judgment, and attribution. We endorse causal Bayesian networks as the best normative framework and as a productive guide to theory building. However, it is incomplete as an account of causal thinking. On the basis of a range of experimental work, we identify three hallmarks of causal reasoning-the role of mechanism, narrative, and mental simulation-all of which go beyond mere probabilistic knowledge. We propose that the hallmarks are closely related. Mental simulations are representations over time of mechanisms. When multiple actors are involved, these simulations are aggregated into narratives.

Causal knowledge and the development of inductive reasoning

We explored the development of sensitivity to causal relations in children's inductive reasoning. Children (5-, 8-, and 12-year-olds) and adults were given trials in which they decided whether a property known to be possessed by members of one category was also possessed by members of (a) a taxonomically related category or (b) a causally related category. The direction of the causal link was either predictive (prey→predator) or diagnostic (predator→prey), and the property that participants reasoned about established either a taxonomic or causal context. There was a causal asymmetry effect across all age groups, with more causal choices when the causal link was predictive than when it was diagnostic. Furthermore, context-sensitive causal reasoning showed a curvilinear development, with causal choices being most frequent for 8-year-olds regardless of context. Causal inductions decreased thereafter because 12-year-olds and adults made more taxonomic choices when reasoning in the taxonomic context. These findings suggest that simple causal relations may often be the default knowledge structure in young children's inductive reasoning, that sensitivity to causal direction is present early on, and that children over-generalize their causal knowledge when reasoning.

Causal explanation in the face of contradiction

Previous work has shown that predictions can be mediated by mechanistic beliefs. The present study shows that such mediation only occurs in the face of contradictory, and not corroborative, evidence. In four experiments, we presented participants with causal statements describing a common-cause structure (E1 ← C → E2). Then we informed them of the states of C and E1 and asked them to judge the likelihood of E2. In Experiments 1 and 2, we manipulated whether the mechanisms supporting the two effects were the same or different, and whether the evidence presented confirmed or contradicted the participants' expectations. The relation between the mechanisms only influenced predictions when evidence contradicted the expectations, but not when it was consistent. In Experiments 3 and 4, we used a common-cause structure with identical mechanisms. We manipulated the order in which predictions were made. When confirmatory predictions were made before contradictory predictions, mechanistic modulation was not observed in the confirmatory case. In contrast, the modulation was found when confirmatory predictions were made after contradictory ones. The results support the contradiction hypothesis that causal structure is revised during prediction, but only in the face of unexpected evidence.

Causal-based property generalization

A central question in cognitive research concerns how new properties are generalized to categories. This article introduces a model of how generalizations involve a process of causal inference in which people estimate the likely presence of the new property in individual category exemplars and then the prevalence of the property among all category members. Evidence in favor of this causal-based generalization (CBG) view included effects of an existing feature's base rate (Experiment 1), the direction of the causal relations (Experiments 2 and 4), the number of those relations (Experiment 3), and the distribution of features among category members (Experiments 4 and 5). The results provided no support for an alternative view that generalizations are promoted by the centrality of the to-be-generalized feature. However, there was evidence that a minority of participants based their judgments on simpler associative reasoning processes.

Where the wild things are: informal experience and ecological reasoning

Category-based induction requires selective use of different relations to guide inferences; this article examines the development of inferences based on ecological relations among living things. Three hundred and forty-six 6-, 8-, and 10-year-old children from rural, suburban, and urban communities projected novel diseases or insides from one species to an ecologically or taxonomically related species; they were also surveyed about hobbies and activities. Frequency of ecological inferences increased with age and with reports of informal exploration of nature, and decreased with population density. By age 10, children preferred taxonomic inferences for insides and ecological inferences for disease, but this pattern emerged earlier among rural children. These results underscore the importance of context by demonstrating effects of both domain-relevant experience and environment on biological reasoning.

An integrated account of generalization across objects and features

Humans routinely make inductive generalizations about unobserved features of objects. Previous accounts of inductive reasoning often focus on inferences about a single object or feature: accounts of causal reasoning often focus on a single object with one or more unobserved features, and accounts of property induction often focus on a single feature that is unobserved for one or more objects. We explore problems where people must make inferences about multiple objects and features, and propose that people solve these problems by integrating knowledge about features with knowledge about objects. We evaluate three computational methods for integrating multiple systems of knowledge: the output combination approach combines the outputs produced by these systems, the distribution combination approach combines the probability distributions captured by these systems, and the structure combination approach combines a graph structure over features with a graph structure over objects. Three experiments explore problems where participants make inferences that draw on causal relationships between features and taxonomic relationships between animals, and we find that the structure combination approach provides the best account of our data.

Inference is bliss: using evolutionary relationship to guide categorical inferences

Three experiments, adopting an evolutionary biology perspective, investigated subjects' inferences about living things. Subjects were told that different enzymes help regulate cell function in two taxa and asked which enzyme a third taxon most likely uses. Experiment 1 and its follow-up, with college students, used triads involving amphibians, reptiles, and mammals (reptiles and mammals are most closely related evolutionarily) and plants, fungi, and animals (fungi are more closely related to animals than to plants). Experiment 2, with 10th graders, also included triads involving mammals, birds, and snakes/crocodilians (birds and snakes/crocodilians are most closely related). Some subjects received cladograms (hierarchical diagrams) depicting the evolutionary relationships among the taxa. The effect of providing cladograms depended on students' background in biology. The results illuminate students' misconceptions concerning common taxa and constraints on their willingness to override faulty knowledge when given appropriate evolutionary evidence. Implications for introducing tree thinking into biology curricula are discussed.

Inductive reasoning

Inductive reasoning entails using existing knowledge or observations to make predictions about novel cases. We review recent findings in research on category-based induction as well as theoretical models of these results, including similarity-based models, connectionist networks, an account based on relevance theory, Bayesian models, and other mathematical models. A number of touchstone empirical phenomena that involve taxonomic similarity are described. We also examine phenomena involving more complex background knowledge about premises and conclusions of inductive arguments and the properties referenced. Earlier models are shown to give a good account of similarity-based phenomena but not knowledge-based phenomena. Recent models that aim to account for both similarity-based and knowledge-based phenomena are reviewed and evaluated. Among the most important new directions in induction research are a focus on induction with uncertain premise categories, the modeling of the relationship between inductive and deductive reasoning, and examination of the neural substrates of induction. A common theme in both the well-established and emerging lines of induction research is the need to develop well-articulated and empirically testable formal models of induction. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website.

Attention as inference: selection is probabilistic; responses are all-or-none samples

Theories of probabilistic cognition postulate that internal representations are made up of multiple simultaneously held hypotheses, each with its own probability of being correct (henceforth, "probability distributions"). However, subjects make discrete responses and report the phenomenal contents of their mind to be all-or-none states rather than graded probabilities. How can these 2 positions be reconciled? Selective attention tasks, such as those used to study crowding, the attentional blink, rapid serial visual presentation, and so forth, were recast as probabilistic inference problems and used to assess how graded, probabilistic representations may produce discrete subjective states. The authors asked subjects to make multiple guesses per trial and used 2nd-order statistics to show that (a) visual selective attention operates in a graded fashion in time and space, selecting multiple targets to varying degrees on any given trial; and (b) responses are generated by a process of sampling from the probabilistic states that result from graded selection. The authors concluded that although people represent probability distributions, their discrete responses and conscious states are products of a process that samples from these probabilistic representations.

Biofeedback mechanisms between shapeable endogen structures and contingent social complexes: The nature of determination for developmental paths

Biofeedback mechanisms (a) between individuals, (b) between the individual and the society structures which shape individual cognitions, and (c) within the individual genetic biochemical circulation, may explain the diversity of trustworthiness potential and the option of mutual trust for every individual in any given society.