Having your cake and eating it too: Towards a Fast and Optimal Method for Analogy Derivation

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The human ability for forming analogies { the ability to see one thing as another { is believed to be a key component of many human cognitive capacities, such as language, learning and reasoning. Humans are very good at forming analogies, yet it is non-trivial to explain how they achieve this given that the computations appear to be quite time consuming. For instance, one of the most influential theories of analogy derivation, Structure-Mapping Theory (SMT) (Gentner, 1983) characterizes analogies as optimally systematic mappings from one representation to another. This theory has been previously proven to be intractable (formally, NP-hard), meaning that computing SMT analogies requires unrealistic amounts of time for all but trivially small representations. However, a large body of empirical research supports the optimality assumption of SMT. This poses the question: If SMT is indeed descriptive of human performance, then how can we explain that humans are able to derive optimal analogies in feasible time? A standard explanation is that humans use a heuristic, which has also been proposed in the literature. A novel explanation is that humans exploit representational parameters to achieve e fficient computation. This thesis provides the first systematic controlled test of the heuristic explanation and a systematic comparison of its performance with that of the parameter explanation. The results establish two main findings: (1) The extent to which the heuristic is capable of computing (close to) optimal analogies is considerably worse than what was previously believed; and (2) an exact algorithm exploiting a key parameter of SMT can compute optimal analogies in a time that matches that of the heuristic. Based on these results we conclude that, in its current form, the heuristic explanation is lacking validity, and the parameter explanation provides a viable alternative which motivates new experimental investigations of analogy derivation.
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