Constructive Solving of Raven's IQ Tests with Analogical Proportions

摘要

The paper shows that a Boolean logic modeling of analogical proportions can serve as a basis for solving quizzes as well as a common and popular type of IQ tests, namely Raven's progressive matrices. They are nonverbal tests supposedly measuring general intelligence. A 3 x 3 Raven matrix exhibits eight geometric pictures displayed as its eight first cells: the remaining ninth cell is empty. In these tests, a set of candidate pictures is also given among which the subject is asked to identify the solution. In this paper, we investigate a general approach allowing to automatically solve Raven's progressive matrices tests. The approach is based on a logical view of analogical proportions, i.e., statements of the form "A is to B as C is to D." We assume that analogical proportions hold between the rows and between the columns of the Raven's matrix. This view can be applied to a feature-based description of the pictures but also, in a number of cases, to a very low level representation, i.e., the pixel level. It appears that the analogical proportion reading just amounts here to a recopy of patterns of feature values that already appear in the data, after checking that there is no conflicting patterns. Implementing this principle, our algorithm builds up the ninth picture, without the help of any set of candidate solutions, and only on the basis of the eight known cells of the Raven matrices. A comparison with other approaches is provided. The ability to construct the missing picture without relying on candidate solutions is a distinctive feature of our work. Moreover, we emphasize the general principle underlying the approach that offers a simple and uniform mechanism applicable to the tests. At this step, the paper makes no claim about the cognitive validity of the approach with respect to the way humans solve such tests.