Why is a raven like a writing desk? How insights from parameterized complexity theory predict human analogical reasoning

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We possess the remarkable capacity to identify and understand relational similarities between the constituent parts of disparate wholes. The analogical mapping process underlying this capacity allows us to draw inferences about objects, actions, and events that we see as analogous to one another. This is believed to be a fundamental aspect of intelligence, found in language, creativity, problem solving, and reasoning. A better understanding of how the brain supports the analogical mapping process carries the potential to better understand the domains where it manifests. However, the most well known model of analogical mapping, called Structure-Mapping Theory, has been shown to be computationally intractable. This is problematic because, assuming that the brain is limited by finite computational resources, brain computation is constrained to be tractable. A solution to this problem has been proposed by van Rooij et al. (2008), who have proven that the computations postulated by SMT are tractable provided that the model parameter o (denoting the number of objects in the analogical match) is relatively small. This proposal yields the prediction that humans can quickly determine good analogical matches in situations where o is small. Moreover, it predicts that performance should deteriorate as o grows because of the inherent intractability of the postulated computations. In this thesis, we set out to test these predictions in a behavioral experiment. Participants were instructed to identify squares that correspond with one another on opposite sides of a divided screen. The results demonstrated that increasing the number of squares resulted in longer response times and less optimal analogical mappings. These findings are consistent with the model’s predictions, and provide support for the FPT-Cognition thesis.
Faculteit der Sociale Wetenschappen