Everyday inductive inferences are often guided by rich background knowledge. Formal models of induction should aim to incorporate this knowledge, and should explain how different kinds of knowledge lead to the distinctive patterns of reasoning found in different inductive contexts. We present a Bayesian framework that attempts to meet both goals and describe four applications of the framework: a taxonomic model, a spatial model, a threshold model, and a causal model. Each model makes probabilistic inferences about the extensions of novel properties, but the priors for the four models are defined over different kinds of structures that capture different relationships between the categories in a domain. Our framework therefore shows how statistical inference can operate over structured background knowledge, and we argue that this interaction between structure and statistics is critical for explaining the power and flexibility of human reasoning.

Everyday knowledge about living things, physical objects and the beliefs and desires of other people appears to be organized into sophisticated systems that are often called intuitive theories. Two long term goals for psychological research are to understand how these theories are mentally represented and how they are acquired. We argue that the language of thought hypothesis can help to address both questions. First, compositional languages can capture the content of intuitive theories. Second, any compositional language will generate an account of theory learning which predicts that theories with short descriptions tend to be preferred. We describe a computational framework that captures both ideas, and compare its predictions to behavioral data from a simple theory learning task. Any comprehensive account of human knowledge must acknowledge

Semantic knowledge is often expressed in the form of intuitive theories, which organize, predict and explain our observations of the world. How are these powerful knowledge structures represented and acquired? We present a framework, logical dimensionality reduction, that treats theories as compressive probabilistic models, attempting to express observed data as a sample from the logical consequences of the theory’s underlying laws and a small number of core facts. By performing Bayesian learning and inference on these models we combine important features of more familiar connectionist and symbolic approaches to semantic cognition: an ability to handle graded, uncertain inferences, together with systematicity and compositionality that support appropriate inferences from sparse observations in novel contexts.

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.

Most models of categorization learn categories defined by characteristic features but some categories are described more naturally in terms of relations. We present a generative model that helps to explain how relational categories are learned and used. Our model learns abstract schemata that specify the relational similarities shared by instances of a category, and our emphasis on abstraction departs from previous theoretical proposals that focus instead on comparison of concrete instances. Our first experiment suggests that abstraction can help to explain some of the findings that have previously been used to support comparison-based approaches. Our second experiment focuses on one-shot schema learning, a problem that raises challenges for comparison-based approaches but is handled naturally by our abstraction-based account. Categories such as family, sonnet, above, betray, and imitate differ in many respects but all of them depend critically on relational information. Members of a family are typically related by blood or marriage, and the lines that make up a sonnet must rhyme with each other according to a certain

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Many researchers have suggested that the psychological complexity of a concept is related to the length of its representation in a language of thought. As yet, however, there are few concrete proposals about the nature of this language. This paper makes one such proposal: the language of thought allows first order quantification (quantification over objects) more readily than second-order quantification (quantification over features). To support this proposal we present behavioral results from a concept learning study inspired by the work of Shepard, Hovland and Jenkins. Humans can learn and think about many kinds of concepts, including natural kinds such as elephant and water and nominal kinds such as grandmother and prime number. Understanding the mental representations that support these abilities is a central challenge for cognitive science. This paper proposes that quantification plays a role in conceptual representation—for example, an animal X qualifies as a predator if there is some animal Y such that X hunts Y. The concepts we consider are much simpler than real-world examples such as predator, but even simple laboratory studies can