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Analogy making is a central construct in human cognition and plays an important role to explain cognitive abilities. While various psychologically or neurally inspired theories for analogical reasoning have been proposed, there is a lack of a logical foundation for analogical reasoning in arti cial intelligence and cognitive science. We aim to close this(More)
We present an approach to analogical reasoning which is inherently dependent on abstraction. While typical cognitive and AI models of analogy perform a direct mapping from objects of the base to objects of the target domain, our model performs mapping via abstraction. Abstraction is calculated as most specific generalization of the base and the target(More)
Anti-unification has often be used as a tool for analogy making. But while first-order anti-unification is too simple for many applications, general higher-order anti-unification is too complex and leads into theoretical difficulties. In this paper we present a restricted framework for higher-order substitutions and show that anti-unification is(More)
We present an account of a process by which different conceptualisations of number can be blended together to form new conceptualisations via recognition of common features, and judicious combination of their distinctive features. The accounts of number are based on Lakoff and Núñez’s cognitively based grounding metaphors for arithmetic. The approach(More)
Intelligence tests often use geometric proportional analogies to examine the intelligence quotient of humans. Completing such a series of geometric figures can be a cognitively demanding task, because the solution requires a suitable conceptualization of the geometric figures. Furthermore, there might exist several, equally correct solutions depending on(More)
The integration of artificial intelligence (AI) within cognitive science (CogSci) necessitates further elaborations on, and modelings of, several indispensable cognitive criteria. We approach this issue by emphasizing the close relation between artificial general intelligence (AGI) and CogSci, and discussing, particularly, “rationality” as one of such(More)
Analogical reasoning has long been seen as a powerful way of extending the reach of ones knowledge. One product of analogical reasoning is analogical learning in which the result of the comparison increases our understanding of some domain. This work describes a method for learning new domain theories by analogy. We use analogies between pairs of problems(More)