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A taxonomy of inductive problems
 Cognitive Science Society
, 2009
"... Inductive inferences about objects, properties, categories, relations, and labels 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 that includes more than thirty inductive problems. The taxonomy ..."
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Inductive inferences about objects, properties, categories, relations, and labels 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 that includes more than thirty inductive problems. The taxonomy helps to clarify the relationships between familiar problems such as identification, stimulus generalization, and categorization, and introduces several novel problems including property identification and object discovery.
DomainCreating Constraints
"... The contributions to this special issue on cognitive development collectively propose ways in which learning involves developing constraints that shape subsequent learning. A learning system must be constrained to learn efficiently, but some of these constraints are themselves learnable. To know how ..."
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The contributions to this special issue on cognitive development collectively propose ways in which learning involves developing constraints that shape subsequent learning. A learning system must be constrained to learn efficiently, but some of these constraints are themselves learnable. To know how something will behave, a learner must know what kind of thing it is. Although this has led previous researchers to argue for domainspecific constraints that are tied to different kinds ⁄ domains, an exciting possibility is that kinds ⁄ domains themselves can be learned. General cognitive constraints, when combined with rich inputs, can establish domains, rather than these domains necessarily preexisting prior to learning. Knowledge is structured and richly differentiated, but its ‘‘skeleton’ ’ must not always be preestablished. Instead, the skeleton may be adapted to fit patterns of cooccurrence, task requirements, and goals. Finally, we argue that for models of development to demonstrate genuine cognitive novelty, it will be helpful for them to move beyond highly preprocessed and symbolic encodings that limit flexibility. We consider two physical models that learn to make tone discriminations. They are mechanistic models that preserve rich spatial, perceptual, dynamic, and concrete information, allowing them to form surprising new classes of hypotheses and encodings.
Using Analogical Representations for Mathematical Concept Formation
"... Abstract. We argue that visual, analogical representations of mathematical concepts can be used by automated theory formation systems to develop further concepts and conjectures in mathematics. We consider the role of visual reasoning in human development of mathematics, and consider some aspects of ..."
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Abstract. We argue that visual, analogical representations of mathematical concepts can be used by automated theory formation systems to develop further concepts and conjectures in mathematics. We consider the role of visual reasoning in human development of mathematics, and consider some aspects of the relationship between mathematics and the visual, including artists using mathematics as inspiration for their art (which may then feed back into mathematical development), the idea of using visual beauty to evaluate mathematics, mathematics which is visually pleasing, and ways of using the visual to develop mathematical concepts. We motivate an analogical representation of number types with examples of “visual ” concepts and conjectures, and present an automated case study in which we enable an automated theory formation program to read this type of visual, analogical representation.
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, 2012
"... doi: 10.3389/fpsyg.2012.00093 Perceptual learning and featurebased approaches to concepts – a critical discussion ..."
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doi: 10.3389/fpsyg.2012.00093 Perceptual learning and featurebased approaches to concepts – a critical discussion
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, 2011
"... One of the challenges for perceptually grounded accounts of highlevel cognition is to explain how people make connections and draw inferences between situations that superficially have little in common. Evidence suggests that people draw these connections even without having explicit, verbalizable ..."
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One of the challenges for perceptually grounded accounts of highlevel cognition is to explain how people make connections and draw inferences between situations that superficially have little in common. Evidence suggests that people draw these connections even without having explicit, verbalizable knowledge of their bases. Instead, the connections are based on subsymbolic representations that are grounded in perception, action, and space. One reason why people are able to spontaneously see relations between situations that initially appear to be unrelated is that their eventual perceptions are not restricted to initial appearances. Training and strategic deployment allow our perceptual processes to deliver outputs that would have otherwise required abstract or formal reasoning. Even without people having any privileged access to the internal operations of perceptual modules, these modules can be systematically altered so as to better serve our highlevel reasoning needs. Moreover, perceptually based processes can be altered in a number of ways to closely approximate formally sanctioned computations. To be concrete about mechanisms of perceptual change, we present 21 illustrations of ways in which we alter, adjust, and augment our perceptual systems with the intention of having them better satisfy our
Estimating Large Numbers
, 2012
"... Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitic ..."
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Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions predict a logtolinear shift: People will either place numbers linearly or will place numbers according to a compressive logarithmic or powershaped function (Barth & Paladino, 2011; Siegler & Opfer, 2003). While about half of people did estimate numbers linearly over this range, nearly all the remaining participants placed 1 million approximately halfway between 1 thousand and 1 billion, but placed numbers linearly across each half, as though they believed that the number words “thousand, million, billion, trillion” constitute a uniformly spaced count list. Participants in this group also tended to be optimistic in evaluations of largely ineffective political strategies, relative to linear numberline placers. The results indicate that the surface structure of number words can heavily influence processes for dealing with numbers in this range, and it can amplify the possibility that analogous surface regularities are partially responsible for parallel phenomena in children. In addition, these results have direct implications for lawmakers and scientists hoping to communicate effectively with the public.