Category-based induction is an inferential mechanism that uses knowledge of conceptual relations in order to estimate how likely is for a property to be projected from one category to another. During the last decades, psychologists have identified several features of this mechanism, and they have proposed different formal models of it. In this article; we propose a new mathematical model for category-based induction based on distances on conceptual spaces. We show how this model can predict most of the properties of (...) this kind of reasoning while providing a solid theoretical foundation for it. We also show that it subsumes some of the previous models proposed in the literature and that it generates new predictions. (shrink)

In this paper, we outline a comprehensive approach to composed analogies based on the theory of conceptual spaces. Our algorithmic model understands analogy as a search procedure and builds upon the idea that analogical similarity depends on a conceptual phenomena called ‘dimensional salience.’ We distinguish between category-based, property-based, event-based, and part-whole analogies, and propose computationally-oriented methods for explicating them in terms of conceptual spaces.

Over the past few decades, cognitive science has identified several forms of reasoning that make essential use of conceptual knowledge. Despite significant theoretical and empirical progress, there is still no unified framework for understanding how concepts are used in reasoning. This paper argues that the theory of conceptual spaces is capable of filling this gap. Our strategy is to demonstrate how various inference mechanisms which clearly rely on conceptual information—including similarity, typicality, and diagnosticity-based reasoning—can be modeled using principles derived from (...) conceptual spaces. Our first topic analyzes the role of expectations in inductive reasoning and their relation to the structure of our concepts. We examine the relationship between using generic expressions in natural language and common-sense reasoning as a second topic. We propose that the strength of a generic can be described by distances between properties and prototypes in conceptual spaces. Our third topic is category-based induction. We demonstrate that the theory of conceptual spaces can serve as a comprehensive model for this type of reasoning. The final topic is analogy. We review some proposals in this area, present a taxonomy of analogical relations, and show how to model them in terms of distances in conceptual spaces. We also briefly discuss the implications of the model for reasoning with concepts in artificial systems. (shrink)

Generic statements play a crucial role in concept learning, communication and education. Despite many efforts, the semantics of generics remain a controversial issue, as they do not seem to fit our standard theories of meaning. In this article, we attempt to shed light on this problem by focusing on how these sentences function in reasoning. Drawing on a distinction between property and diagnostic generics, we defend three theses: First, property generics are not about facts but express relations between concepts. Second, (...) generics play an important role in everyday reasoning by interacting with our expectations about the world. Third, diagnostic generics emphasise properties that separate the category in the generics from other categories in the same contrast class. We use the theory of conceptual spaces to advance measures of typicality and diagnosticity capable of modelling different aspects of generics and apply them to the modifier effect and the inverse conjunction fallacy. Finally, we discuss the pragmatics of generics. (shrink)