Nature and facts about natural and artifactual categories: Sex differences in the semantic priming paradigm

There is abundant evidence from behavioral and neurophysiological experiments for the distinction of natural versus artifactual categories and a gender-specific difference: women’s performances in cognitive tasks increase when natural categories are used, whereas men’s performances increase with artifactual categories. Here, we used the semantic priming paradigm to study retrieval processes by presenting category labels as primes and exemplars as targets. Overall, in two experiments we found larger priming effects for natural than for artifactual categories. In addition, females showed positive priming effects for natural but negative effects for artifactual categories, whereas males showed positive priming effects for both categories. This pattern matches with that from other tasks and can be interpreted as evidence that the findings from these other tasks are, at least partially, indeed due to different representations or processing modes for males and females and not (exclusively) due to—for example—different familiarity with a category. In a further experiment, we showed that the found pattern for females can be manipulated by focusing on perceptual vs. functional features. The results can be interpreted as first evidence that there are (eventually in addition to different “crystallized” semantic structures) specific default processing modes that differ for males and females.     

Is ZF a hack?: Comparing the complexity of some (formalist interpretations of) foundational systems for mathematics

This paper presents Automath encodings (which are also valid in LF/λP) of various kinds of foundations of mathematics. Then it compares these encodings according to their size, to find out which foundation is the simplest.

The systems analyzed in this way are two kinds of set theory (ZFC and NF), two systems based on Church's higher order logic (Isabelle/Pure and HOL), three kinds of type theory (the calculus of constructions, Luo's extended calculus of constructions, and Martin-Löf's predicative type theory) and one foundation based on category theory.

The conclusions of this paper are that the simplest system is type theory (the calculus of constructions), but that type theories that know about serious mathematics are not simple at all. In that case the set theories are the simplest. If one looks at the number of concepts needed to explain such a system, then higher order logic is the simplest, with twenty-five concepts. On the other side of the scale, category theory is relatively complex, as is Martin-Löf's type theory.

(The full Automath sources of the contexts described in this paper are one the web at http://www.cs.ru.nl/~freek/zfc-etc/.)     

Beyond common features: the role of roles in determining similarity

Historically, accounts of object representation and perceived similarity have focused on intrinsic features. Although more recent accounts have explored how objects, scenes, and situations containing common relational structures come to be perceived as similar, less is known about how the perceived similarity of parts or objects embedded within these relational systems is affected. The current studies test the hypothesis that objects situated in common relational systems come to be perceived as more similar. Similarity increases most for objects playing the same role within a relation (e.g., predator), but also increases for objects playing different roles within the same relation (e.g., the predator or prey role in the hunts relation) regardless of whether the objects participate in the same instance of the relation. This pattern of results can be captured by extending existing models that extract meaning from text corpora so that they are sensitive to the verb-specific thematic roles that objects fill. Alternative explanations based on analogical and inferential processes are also considered, as well as the implications of the current findings to research in language processing, decision making, and category learning.     

On three arguments against categorical structuralism

Some mathematicians and philosophers contend that set theory plays a foundational role in mathematics. However, the development of category theory during the second half of the twentieth century has encouraged the view that this theory can provide a structuralist alternative to set-theoretical foundations. Against this tendency, criticisms have been made that category theory depends on set-theoretical notions and, because of this, category theory fails to show that set-theoretical foundations are dispensable. The goal of this paper is to show that these criticisms are misguided by arguing that category theory is entirely autonomous from set theory.     

The development of category learning strategies: What makes the difference?

Category learning can be achieved by identifying common features among category members, distinctive features among non-members, or both. These processes are psychologically and computationally distinct, and may have implications for the acquisition of categories at different hierarchical levels. The present study examines an account of children’s difficulty in acquiring categories at the subordinate level grounded on these distinct comparison processes. Adults and children performed category learning tasks in which they were exposed either to pairs of objects from the same novel category or pairs of objects from different categories. The objects were designed so that for each category learning task, two features determined category membership whereas two other features were task irrelevant. In the learning stage participants compared pairs of objects noted to be either from the same category or from different categories. Object pairs were chosen so that the objective amount of information provided to the participants was identical in the two learning conditions. We found that when presented only with object pairs noted to be from the same category, young children (6 ? YO ? 9.5) learned the novel categories just as well as older children (10 ? YO ? 14) and adults. However, when presented only with object pairs known to be from different categories, unlike older children and adults, young children failed to learn the novel categories. We discuss cognitive and computational factors that may give rise to this comparison bias, as well as its expected outcomes.     

Cognitive Style,Creativity Framing and Effects

This study investigates how individuals with different cognitive styles respond to choices involving framing effects. The results suggest that cognitive style as defined by Kirton (1976) is far more complex than previous studies indicate. Kirton characterises “Innovators” as rule breakers and “Adaptors” as conformists. The most important finding of this study is that in some decision contexts, Innovators and Adaptors exhibit similar preferences for rule breaking. In other situations, Adaptors actually prefer non‐conformity in comparison to Innovators. The study analysed responses from 146 university students and professional managers to 25 binary choices involving investment decisions, job choices and travel routes. The questions were constructed to reveal significant reversals of preference related to risk and attribute based framing effects. Additionally, some questions were constructed to reveal preferences for certain operational aspects of creativity. Overall, the results suggest that framing effects may provide an important tool for unlocking individual creativity in organisations, as long as cognitive style and context are carefully taken into account.     

More is more: The relationship between vocabulary size and word extension

This study experimentally tested the relationship between children’s lexicon size and their ability to learn new words within the domain of color. We manipulated the size of 25 20-month-olds’ color lexicons by training them with two, four, or six different color words over the course of eight training sessions. We subsequently tested children’s ability to extend new color words to new instances. We found that training with a broader number of color words led to increased extension of new words. The results suggest that children’s learning history predicts their ability to learn new words within domains.     

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.     

Do Additional Features Help or Hurt Category Learning? The Curse of Dimensionality in Human Learners

The curse of dimensionality, which has been widely studied in statistics and machine learning, occurs when additional features cause the size of the feature space to grow so quickly that learning classification rules becomes increasingly difficult. How do people overcome the curse of dimensionality when acquiring real‐world categories that have many different features? Here we investigate the possibility that the structure of categories can help. We show that when categories follow a family resemblance structure, people are unaffected by the presence of additional features in learning. However, when categories are based on a single feature, they fall prey to the curse, and having additional irrelevant features hurts performance. We compare and contrast these results to three different computational models to show that a model with limited computational capacity best captures human performance across almost all of the conditions in both experiments.     

Categorical and dimensional perceptions in decoding emotional facial expressions

We investigated whether categorical perception and dimensional perception can co-occur while decoding emotional facial expressions. In Experiment 1, facial continua with endpoints consisting of four basic emotions (i.e., happiness–fear and anger–disgust) were created by a morphing technique. Participants rated each facial stimulus using a categorical strategy and a dimensional strategy. The results show that the happiness–fear continuum was divided into two clusters based on valence, even when using the dimensional strategy. Moreover, the faces were arrayed in order of the physical changes within each cluster. In Experiment 2, we found a category boundary within other continua (i.e., surprise–sadness and excitement–disgust) with regard to the arousal and valence dimensions. These findings indicate that categorical perception and dimensional perception co-occurred when emotional facial expressions were rated using a dimensional strategy, suggesting a hybrid theory of categorical and dimensional accounts.