Analogy-Making for Solving IQ Tests: A Logical View

Among the diverse processes at work in human cognition, the ability to establish analogies plays a crucial role and is often evaluated via IQ tests where an incomplete sequence has to be completed with a suitable item. This has motivated the AI community for developing various computational models of analogy-making. A Boolean logic view of analogical proportions (a basic form of analogical statements of the form "a is to b as c is to d") has been recently proposed and extended to another logical proportion, namely paralogical proportion (stating that "what a and b have in common, c and d have it also"). When used in combination, these 2 proportions provide an enhanced power to complete IQ tests. This Boolean modeling essentially relies on the assessment of the differences and similarities between the items involved, and in the case of analogy, satisfies the expected properties of an analogical proportion. An extension to multiple-valued features has also been defined, reinforcing their scope of applications. It is then possible to complete, in a deterministic manner, some incomplete proportions where the last item d is missing. In this paper, we show how this can be the basis of a simple inference paradigm that provides a rigorous way to solve representative analogy-based IQ tests by computing the missing items rather than by choosing in a list of options. The result of the analogical/paralogical inference depends on the way the items are represented. The paper discusses how this approach can be used in analogy-making for both determining missing items in proportions and laying bare the relation linking the components of such proportions. The novelty of the approach is stressed w.r.t. other proposals existing in the literature.