Having your cake and eating it too: Towards a Fast and Optimal Method for Analogy Derivation
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2013-08-02
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en
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Abstract
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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Faculteit der Sociale Wetenschappen