A model for analogical reasoning
A theory of analogical reasoning is proposed in which the elements of a set of concepts, e.g., animals, are represented as points in a multidimensional Euclidean space. Four elements A,B,C,D, are in an analogical relationship A:B::C:D if the vector distance from A to B is the same as that from C to D. Given three elements A,B,C, an ideal solution point I for A:B::C:? exists. In a problem A:B::C:D1, …, Di, …, Dn, the probability of choosing Di as the best solution is a monotonic decreasing function of the absolute distance of Di from I. A stronger decision rule incorporating a negative exponential function in Luce's choice rule is also proposed. Both the strong and weak versions of the theory were supported in two experiments where Ss rank-ordered the alternatives in problems A:B::C:D1,D2, D3D4. In a third experiment the theory was applied and further tested in teaching new concepts by analogy.