The acquiring of formal, abstract mathematical concepts by students may be said to be one of the major goals of mathematics teaching. How are such abstract concepts acquired? How does this formal knowledge interact with the students' intuitive knowledge of mathematics? How does the transition from informal mathematical knowledge to formal mathematical knowledge take place? This paper reports on...

Prior work suggests that our understanding of how things work ("intuitive physics") and how people work ("intuitive psychology") are distinct domains of human cognition. Here we directly test the dissociability of these two domains by investigating knowledge of intuitive physics and intuitive psychology in adults with Williams syndrome (WS) - a genetic developmental disorder characterized by se...

Research on human infants, adult nonhuman primates, and children and adults in diverse cultures provides converging evidence for four systems at the foundations of human knowledge. These systems are domain specific and serve to represent both entities in the perceptible world (inanimate manipulable objects and animate agents) and entities that are more abstract (numbers and geometrical forms). ...

Abstract. This paper investigates meta structures, schema-level graphs that abstract connectivity information among a set of entities in a knowledge graph. Meta structures are useful in a variety of knowledge discovery tasks ranging from relatedness explanation to data retrieval. We formalize the meta structure computation problem and devise efficient automata-based algorithms. We introduce a m...

One of the hallmarks of human intelligence is its flexibility. While computers have achieved better-than-human performance in various games, such as Chess, Jeopardy, or Go, there is no single algorithm yet that works in all of these cases. Humans, however, can excel at all of these games, and many other tasks. We believe that bridging the gap between human and machine intelligence requires two ...

Sider argues that, of maximalism and quantifier variance, the latter promises to let us make better sense of neo-Fregeanism. I argue that neo-Fregeans should, and seemingly do, reject quantifier variance. If they must choose between these two options, they should choose maximalism. 1: Introduction Benacerraf’s problem lies at the heart of philosophy of mathematics: the truth of mathematical sta...