A taxonomy of inductive problems

Abstract

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.Keywords: induction; semantic cognition; generalization; categorization; identification; reasoning Attempts to systematize knowledge have proven useful in several fields. Mendeleev presented a periodic table of the chemical elements that helped to clarify relationships between known elements and that made predictions about the existence of new elements. Adelson and Bergen [1] developed a "periodic table" of early vision that maps out a space of visual computations and identifies several that had previously received little attention. This paper aims to make a similar contribution to the study of inductive inference. We describe a taxonomy of inductive problems that aims to clarify the relationships between different problems and to highlight problems that have previously been overlooked.An inductive inference goes beyond the information given and reaches a conclusion that is likely but not certain given the available evidence. Inferences of this kind are relevant to almost every area of cognition, and take place, for example, when humans predict the motion of an occluded object, guess the meaning of a novel word, or decide how to grasp an object that is encountered for the first time. We will not discuss vision, language, or motor control, but instead focus on a cluster of problems from an area that has been called semantic cognition. Research in this area aims to capture knowledge about objects and their properties, categories or collections of objects, relationships between objects, and word meanings. Accounts of semantic cognition differ in many respects but most of them rely on six basic notions: objects, properties, categories, relations, labels, and truth values. Our taxonomy takes these six notions as a starting point and attempts to chart the space of inductive problems that can be posed given a commitment to these notions. Two familiar problems that belong to this space are categorization and property induction, or deciding whether an object has an unobserved property.Most psychological work on inductive inference focuses on a single inductive problem, but some existing frameworks address multiple problems [7]. For example, exemplar models that formalize objects as points in a multidimensional space have been used to account for several problems including identification, stimulus generalization, recognition, and categorization [13]. Our taxonomy includes all of these problems along with many others. Since we aim to characterize inductive problems rather than to describe the psycholog...

Category-based induction from similarity of neural activation

“…1) in favor of the definition of conditional probability (Eq. 2) distinguishes our approach from the Bayesian modeling that has clarified several aspects of inductive reasoning (Kemp & Jern, 2013). Our approach is also distinguished by its appeal to neural similarity as a means of deriving the probabilities needed to make predictions about subjects' judgment.…”

The Distinction Between Inductive Confidence and Inferences in Property Induction

“…Examining inductive confidences can reveal metacognition in inductive reasoning. There are various inductive problems (Hayes, Heit, & Swendsen, 2010;Kemp & Jern, 2013). Thus, it is necessary to examine…”

“…The distinction between inductive confidences and inferences 3 Inductive reasoning is that people project information from known cases to the unknown (Heit, 2000;Hayes, Heit, & Swendsen, 2010;Kemp & Jern, 2013). One main research topic in inductive reasoning is category-based property induction (Hayes, Heit, & Swendsen, 2010;Kemp & Jern, 2013;Medin, et al, 2003;Osherson, et al, 1990;Sloman & Lagnado, 2005).…”

“…One main research topic in inductive reasoning is category-based property induction (Hayes, Heit, & Swendsen, 2010;Kemp & Jern, 2013;Medin, et al, 2003;Osherson, et al, 1990;Sloman & Lagnado, 2005). This typically involves making an inference about the properties of some conclusion category, based on knowledge of the properties of some premise category or set of categories (Hayes, Heit, & Swendsen, 2010).…”

“…Moreover, in relevance-based inductions, the influence of relevance similarity on inductive inferences depended on relevance strength, and relevance strength affected inductive inferences and confidences in the different ways. These findings will arouse further research on metacognition in inductive reasoning in the future.Keywords: property induction; relevance strength; relevance similarity; inductive inference; inductive confidence.The distinction between inductive confidences and inferences 3 Inductive reasoning is that people project information from known cases to the unknown (Heit, 2000;Hayes, Heit, & Swendsen, 2010;Kemp & Jern, 2013). One main research topic in inductive reasoning is category-based property induction (Hayes, Heit, & Swendsen, 2010;Kemp & Jern, 2013;Medin, et al, 2003;Osherson, et al, 1990;Sloman & Lagnado, 2005).…”