Instantiated features and the use of "rules."

Classification "rules" in expert and everyday discourse are usually deficient by formal standards, lacking explicit decision procedures and precise terms. The authors argue that a central function of such weak rules is to focus on perceptual learning rather than to provide definitions. In 5 experiments, transfer following learning of family resemblance categories was influenced more by familiar-appearing features than by novel-appearing features equally acceptable under the rule. This occurred both when rules were induced and when rules were given at the beginning of instruction. To model this and other phenomena in categorization, features must be represented on 2 levels: informational and instantiated. These 2 feature levels are crucial to provide broad generalization while reflecting the known peculiarities of a complex world.     

Children’s Developing Understanding of the Conventionality of Rules

Much research has investigated how children relate to norms taught to them by adult authorities. Very few studies have investigated norms that arise out of children’s own peer interactions. In two studies, we investigated how 5- and 7-year-old children teach, enforce, and understand rules that they either created themselves or were taught by an adult. Children (N = 240) were asked to either invent game rules on their own or were taught these exact same rules by an adult (yoked design). Children of both ages enforced and transmitted the rules in a normative way, regardless of whether they had invented them or were taught the rules by an adult, suggesting that they viewed even their own self-made rules as normatively binding. However, creating the rules led 5-year-old children to understand them as much more changeable as compared with adult-taught rules. Seven-year-olds, in contrast, regarded both kinds of rules as equally changeable, indeed allowing fewer changes to their self-created rules than 5-year-olds. While the process of creating rules seemed to enlighten preschoolers’ understanding of the conventionality of the rules, school-aged children regarded both self-created rules and adult-taught rules in a similar manner, suggesting a deeper understanding of rule normativity as arising from social agreement and commitment.     

Information from multiple modalities helps 5‐month‐olds learn abstract rules

By 7 months of age, infants are able to learn rules based on the abstract relationships between stimuli ( Marcus et al ., 1999 ), but they are better able to do so when exposed to speech than to some other classes of stimuli. In the current experiments we ask whether multimodal stimulus information will aid younger infants in identifying abstract rules. We habituated 5‐month‐olds to simple abstract patterns (ABA or ABB) instantiated in coordinated looming visual shapes and speech sounds (Experiment 1), shapes alone (Experiment 2), and speech sounds accompanied by uninformative but coordinated shapes (Experiment 3). Infants showed evidence of rule learning only in the presence of the informative multimodal cues. We hypothesize that the additional evidence present in these multimodal displays was responsible for the success of younger infants in learning rules, congruent with both a Bayesian account and with the Intersensory Redundancy Hypothesis.     

More than a matter of getting ‘unstuck’: flexible thinkers use more abstract representations than perseverators

Why do people perseverate, repeating prior behaviours that are no longer appropriate? Many accounts point to isolated deficits in processes such as inhibition or attention. We instead posit a fundamental difference in rule representations: flexible switchers use active representations that rely on later‐developing prefrontal cortical areas and are more abstract, whereas perseverators use latent representations that rely on earlier‐developing posterior cortical and subcortical areas and are more stimulus‐specific. Thus, although switchers and perseverators should apply the rules they use to familiar stimuli equally reliably, perseverators should show unique limitations in generalizing their rules to novel stimuli, a process that requires abstract representations. Two behavioural experiments confirmed this counterintuitive prediction early in development. Three‐year‐old children sorted cards by one rule, were asked to switch to another rule, and then were asked simply to continue their behaviour, with novel cards. Perseverators applied the rule they were using (the first rule) just as reliably as switchers applied the rule they were using (the second rule) with familiar cards; however, only switchers generalized their rule to novel cards. This finding supports an early link between active representations that support switching and abstract representations that support generalization. We interpret this synergy in terms of prefrontal cortical development.     

Typicality in logically defined categories: Exemplar-similarity versus rule instantiation

A rule-instantiation model and a similarity-to-exemplars model were contrasted in terms of their predictions of typicality judgments and speeded classifications for members of logically defined categories. In Experiment 1, subjects learned a unidimensional rule based on the size of objects. It was assumed that items that maximally instantiated the rule were those farthest from the category boundary that separated small and large stimuli. In Experiment 2, subjects learned a disjunctive rule of the form "x or y or both". It was assumed that items that maximally instantiated the rule were those with both positive values (x and y). In both experiments, the frequency with which different exemplars were presented during classification learning was manipulated across conditions. These frequency manipulations exerted a major impact on subjects' postacquisition goodness-of-example judgments, and they also influenced reaction times in a speeded classification task. The results could not be predicted solely on the basis of the degree to which the rules were instantiated. The goodness judgments were predicted fairly well by a mixed exemplar model involving both relative-similarity and absolute-similarity components. It was concluded that even for logically defined concepts, stored exemplars may form a major component of the category representation.     

Influence of familiar features on diagnosis: instantiated features in an applied setting

Medical diagnosis can be viewed as a categorization task. There are two mechanisms whereby humans make categorical judgments: "analytical reasoning," based on explicit consideration of features and "nonanalytical reasoning," an unconscious holistic process of matching against prior exemplars. However, there is evidence that prior experience can also operate at the level of individual "instantiated" features (Brooks & Hannah, 2006). The present studies examined instantiated features in medical diagnosis. Four "pseudopsychiatric" conditions, each described by four characteristic features, were taught to undergraduate psychology students. They practiced on additional cases, then were tested on new cases with features from two conditions. In Experiment 1, diagnoses associated with familiar features presented one or three times during practice were assigned a higher probability than those with novel features. Experiment 2 showed that the impact of feature frequency was dependent on its consistency with the case diagnosis. Experiment 3 showed that the effect of feature familiarity was not confined to cases with two equiprobable diagnoses. Experiment 4 showed that the effect remained after a 24 hour delay. These four studies demonstrated that features seen in practice have a greater influence on diagnosis than novel synonyms. In fact, seeing a feature once within the appropriate context (a patient case in which it is a member of the primary diagnosis) was sufficient to form a diagnostic association equivalent to instantiations seen four times in a different context. The results of these studies have implications for theories of categorization and for teaching clinical reasoning.     

The effects of statistical training on thinking about everyday problems

People possess an abstract inferential rule system that is an intuitive version of the law of large numbers. Because the rule system is not tied to any particular content domain, it is possible to improve it by formal teaching techniques. We present four experiments that support this view. In Experiments 1 and 2, we taught subjects about the formal properties of the law of large numbers in brief training sessions in the laboratory and found that this increased both the frequency and the quality of statistical reasoning for a wide variety of problems of an everyday nature. In addition, we taught subjects about the rule by a “guided induction” technique, showing them how to use the rule to solve problems in particular domains. Learning from the examples was abstracted to such an extent that subjects showed just as much improvement on domains where the rule was not taught as on domains where it was. In Experiment 3, the ability to analyze an everyday problem with reference to the law of large numbers was shown to be much greater for those who had several years of training in statistics than for those who had less. Experiment 4 demonstrated that the beneficial effects of formal training in statistics may hold even when subjects are tested completely outside of the context of training. In general, these four experiments support a rather “formalist” theory of reasoning: people reason using very abstract rules, and their reasoning about a wide variety of content domains can be affected by direct manipulation of these abstract rules.     

Producing biased diagnoses with unambiguous stimuli: The importance of feature instantiations

In this article, the authors demonstrate a laboratory analogue of medical diagnostic biasing (V. R. LeBlanc, G. R. Norman, & L. R. Brooks, 2001) in 2 experiments and explore the basis of this effect. Before categorizing novel exemplars, participants first evaluated the likelihood that the item was a member of the category suggested on that trial: either the correct category or a plausible alternative category. This was sufficient to produce a substantial bias toward the suggested category despite the use of unambiguous stimuli, explicit rules, and unhurried conditions--each of which would be likely to limit diagnostic bias. The authors argue that the production of this effect requires distinguishing between particular feature instantiations and more abstract representations of those features as well as allowing people to adopt a particular decision strategy mediating the use of instantiated features: a feature-recognition heuristic.     

Artificial grammar learning in children: abstraction of rules or sensitivity to perceptual features?

We examined sensitivity to grammatical sequences of colors in an artificial grammar learning task in a sample of 120 children aged between 5 and 8 years. The aim of the experiment was to test whether the children would preferentially learn the specific salient features of the items they were exposed to or the rules that generated these items. The children were divided into two experimental groups (identical grammar but training items differing in their surface features) and a control group (random items). The results showed that regardless of age, participants learned the most frequent salient features of the items, as well as some kind of abstract relational information. However, the 8-year-olds presented a more complex result profile, with one of the experimental groups apparently developing sensitivity to grammatical rules. These results are discussed with reference to the main current models of implicit learning. Overall, the results provided more support for stimulus-specific processing models than for rule-based models.     

Explanation-based learning in infancy

In explanation-based learning (EBL), domain knowledge is leveraged in order to learn general rules from few examples. An explanation is constructed for initial exemplars and is then generalized into a candidate rule that uses only the relevant features specified in the explanation; if the rule proves accurate for a few additional exemplars, it is adopted. EBL is thus highly efficient because it combines both analytic and empirical evidence. EBL has been proposed as one of the mechanisms that help infants acquire and revise their physical rules. To evaluate this proposal, 11- and 12-month-olds (n?=?260) were taught to replace their current support rule (that an object is stable when half or more of its bottom surface is supported) with a more sophisticated rule (that an object is stable when half or more of the entire object is supported). Infants saw teaching events in which asymmetrical objects were placed on a base, followed by static test displays involving a novel asymmetrical object and a novel base. When the teaching events were designed to facilitate EBL, infants learned the new rule with as few as two (12-month-olds) or three (11-month-olds) exemplars. When the teaching events were designed to impede EBL, however, infants failed to learn the rule. Together, these results demonstrate that even infants, with their limited knowledge about the world, benefit from the knowledge-based approach of EBL.     

Sequential learning and rule abstraction in Bengalese finches

The Bengalese finch (Lonchura striata var. domestica) is a species of songbird. Males sing courtship songs with complex note-to-note transition rules, while females discriminate these songs when choosing their mate. The present study uses serial reaction time (RT) to examine the characteristics of the Bengalese finches’ sequential behaviours beyond song production. The birds were trained to produce the sequence with an “A–B–A” structure. After the RT to each key position was determined to be stable, we tested the acquisition of the trained sequential response by presenting novel and random three-term sequences (random test). We also examined whether they could abstract the embedded rule in the trained sequence and apply it to the novel test sequence (abstract test). Additionally, we examined rule abstraction through example training by increasing the number of examples in baseline training from 1 to 5. When considered as (gender) groups, training with 5 examples resulted in no statistically significant differences in the abstract tests, while statistically significant differences were observed in the random tests, suggesting that the male birds learned the trained sequences and transferred the abstract structure they had learned during the training trials. Individual data indicated that males, as opposed to females, were likely to learn the motor pattern of the sequence. The results are consistent with observations that males learn to produce songs with complex sequential rules, whereas females do not.     

Traces of reasoning with pragmatic schemas

Holyoak and Cheng's (1995) account of Wason's (1966) selection task was evaluated by testing participants' recognition memory for the rule. To accommodate the finding that participants' selections are systematically influenced by manipulating their perspective on the rule to be tested, Holyoak and Cheng put forward a development of Pragmatic Reasoning Schema (PRS) theory, according to which the rule being tested is mapped onto different schematic rules depending on the perspective taken. The instantiated schema then becomes the basis for reasoning, and the different schemas encourage the selection of different cases. We hypothesised that if participants interpret the rule by instantiating a particular schema, then they should falsely recognise a sentence corresponding to the instantiated schema a short time after performing the task. An experimental test provided limited support for this hypothesis.     

Phonological Concept Learning

Linguistic and non‐linguistic pattern learning have been studied separately, but we argue for a comparative approach. Analogous inductive problems arise in phonological and visual pattern learning. Evidence from three experiments shows that human learners can solve them in analogous ways, and that human performance in both cases can be captured by the same models. We test GMECCS (Gradual Maximum Entropy with a Conjunctive Constraint Schema), an implementation of the Configural Cue Model (Gluck & Bower, 1988a ) in a Maximum Entropy phonotactic‐learning framework (Goldwater & Johnson, 2003 ; Hayes & Wilson, 2008 ) with a single free parameter, against the alternative hypothesis that learners seek featurally simple algebraic rules (“rule‐seeking”). We study the full typology of patterns introduced by Shepard, Hovland, and Jenkins ( 1961 ) (“SHJ”), instantiated as both phonotactic patterns and visual analogs, using unsupervised training. Unlike SHJ, Experiments 1 and 2 found that both phonotactic and visual patterns that depended on fewer features could be more difficult than those that depended on more features, as predicted by GMECCS but not by rule‐seeking. GMECCS also correctly predicted performance differences between stimulus subclasses within each pattern. A third experiment tried supervised training (which can facilitate rule‐seeking in visual learning) to elicit simple rule‐seeking phonotactic learning, but cue‐based behavior persisted. We conclude that similar cue‐based cognitive processes are available for phonological and visual concept learning, and hence that studying either kind of learning can lead to significant insights about the other.     

Rules vs. analogy in English past tenses: a computational/experimental study

Are morphological patterns learned in the form of rules? Some models deny this, attributing all morphology to analogical mechanisms. The dual mechanism model (Pinker, S., & Prince, A. (1998). On language and connectionism: analysis of a parallel distributed processing model of language acquisition. Cognition, 28, 73-193) posits that speakers do internalize rules, but that these rules are few and cover only regular processes; the remaining patterns are attributed to analogy. This article advocates a third approach, which uses multiple stochastic rules and no analogy. We propose a model that employs inductive learning to discover multiple rules, and assigns them confidence scores based on their performance in the lexicon. Our model is supported over the two alternatives by new "wug test" data on English past tenses, which show that participant ratings of novel pasts depend on the phonological shape of the stem, both for irregulars and, surprisingly, also for regulars. The latter observation cannot be explained under the dual mechanism approach, which derives all regulars with a single rule. To evaluate the alternative hypothesis that all morphology is analogical, we implemented a purely analogical model, which evaluates novel pasts based solely on their similarity to existing verbs. Tested against experimental data, this analogical model also failed in key respects: it could not locate patterns that require abstract structural characterizations, and it favored implausible responses based on single, highly similar exemplars. We conclude that speakers extend morphological patterns based on abstract structural properties, of a kind appropriately described with rules.     

What do Raven's Matrices measure? An analysis in terms of sex differences

Although it is sometimes claimed that Raven's Matrices provide an almost pure measure of g, there is evidence that the easier items in the Standard Progressive Matrices and in Set I of the Advanced Matrices measure a perceptual or Gestalt factor distinct from the more analytic items in the rest of the tests. There is also, however, both factor analytic and experimental evidence that these analytic items fall into two partially separate groups, distinguishable by the type of rule needed for their solution in the analysis proposed by Carpenter, Just, and Schell (1990) [Carpenter, P. A., Just, M. A., Schell, P. (1990). What one intelligence test measures: A theoretical account of the processing in the Raven's Progressive Matrices Test. Psychological Review, 97, 404–431]. Re-analysis of published data suggests a new source of evidence for this further distinction: males do better than females on items requiring an addition/subtraction or distribution of two rule, but there is no sex difference on items requiring pairwise progression or distribution of three rules. A specially designed experiment confirmed this pattern of results.     

Robustness of the rule-learning effect in 7-month-old infants: A close,multicenter replication of Marcus et al. (1999)

We conducted a close replication of the seminal work by Marcus and colleagues from 1999, which showed that after a brief auditory exposure phase, 7-month-old infants were able to learn and generalize a rule to novel syllables not previously present in the exposure phase. This work became the foundation for the theoretical framework by which we assume that infants are able to learn abstract representations and generalize linguistic rules. While some extensions on the original work have shown evidence of rule learning, the outcomes are mixed, and an exact replication of Marcus et al.'s study has thus far not been reported. A recent meta-analysis by Rabagliati and colleagues brings to light that the rule-learning effect depends on stimulus type (e.g., meaningfulness, speech vs. nonspeech) and is not as robust as often assumed. In light of the theoretical importance of the issue at stake, it is appropriate and necessary to assess the replicability and robustness of Marcus et al.'s findings. Here we have undertaken a replication across four labs with a large sample of 7-month-old infants (N = 96), using the same exposure patterns (ABA and ABB), methodology (Headturn Preference Paradigm), and original stimuli. As in the original study, we tested the hypothesis that infants are able to learn abstract “algebraic” rules and apply them to novel input. Our results did not replicate the original findings: infants showed no difference in looking time between test patterns consistent or inconsistent with the familiarization pattern they were exposed to.     

The effects of cumulative practice on mathematics problem solving

This study compared three different methods of teaching five basic algebra rules to college students. All methods used the same procedures to teach the rules and included four 50-question review sessions interspersed among the training of the individual rules. The differences among methods involved the kinds of practice provided during the four review sessions. Participants who received cumulative practice answered 50 questions covering a mix of the rules learned prior to each review session. Participants who received a simple review answered 50 questions on one previously trained rule. Participants who received extra practice answered 50 extra questions on the rule they had just learned. Tests administered after each review included new questions for applying each rule (application items) and problems that required novel combinations of the rules (problem-solving items). On the final test, the cumulative group outscored the other groups on application and problem-solving items. In addition, the cumulative group solved the problem-solving items significantly faster than the other groups. These results suggest that cumulative practice of component skills is an effective method of training problem solving.     

Quantifying disablers in reasoning with universal and existential rules

People accept conclusions of valid conditional inferences (e.g., if p then q, p therefore q) less, the more disablers (circumstances that prevent q to happen although p is true) exist. We investigated whether rules that through their phrasing exclude disablers evoke higher acceptance ratings than rules that do not exclude disablers. In three experiments we re-phrased content-rich conditionals from the literature as either universal or existential rules and embedded these rules in Modus Ponens and Modus Tollens inferences. In Experiments 2 and 3, we also used abstract rules. The acceptance of conclusions increased when the rule was phrased with “all” instead of “some” and the number of disablers had a higher impact on existential rules than on universal rules. Further, the effect of quantifier was more pronounced for abstract rules and when tested within subjects. We discuss the relevance of phrasing, quantifiers and knowledge on reasoning.     

The profile of abstract rule learning in infancy: Meta‐analytic and experimental evidence

Everyone agrees that infants possess general mechanisms for learning about the world, but the existence and operation of more specialized mechanisms is controversial. One mechanism—rule learning—has been proposed as potentially specific to speech, based on findings that 7‐month‐olds can learn abstract repetition rules from spoken syllables (e.g. ABB patterns: wo‐fe‐fe, ga‐tu‐tu…) but not from closely matched stimuli, such as tones. Subsequent work has shown that learning of abstract patterns is not simply specific to speech. However, we still lack a parsimonious explanation to tie together the diverse, messy, and occasionally contradictory findings in that literature. We took two routes to creating a new profile of rule learning: meta‐analysis of 20 prior reports on infants’ learning of abstract repetition rules (including 1,318 infants in 63 experiments total), and an experiment on learning of such rules from a natural, non‐speech communicative signal. These complementary approaches revealed that infants were most likely to learn abstract patterns from meaningful stimuli. We argue that the ability to detect and generalize simple patterns supports learning across domains in infancy but chiefly when the signal is meaningfully relevant to infants’ experience with sounds, objects, language, and people.     

Children reading spoken words: interactions between vocabulary and orthographic expectancy

There is an established association between children's oral vocabulary and their word reading but its basis is not well understood. Here, we present evidence from eye movements for a novel mechanism underlying this association. Two groups of 18 Grade 4 children received oral vocabulary training on one set of 16 novel words (e.g., ‘nesh’, ‘coib’), but no training on another set. The words were assigned spellings that were either predictable from phonology (e.g., nesh) or unpredictable (e.g., koyb). These were subsequently shown in print, embedded in sentences. Reading times were shorter for orally familiar than unfamiliar items, and for words with predictable than unpredictable spellings but, importantly, there was an interaction between the two: children demonstrated a larger benefit of oral familiarity for predictable than for unpredictable items. These findings indicate that children form initial orthographic expectations about spoken words before first seeing them in print. A video abstract of this article can be viewed at: https://youtu.be/jvpJwpKMM3E .