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Constructive solving of Raven's IQ tests with analogical proportions

Correa Beltran, William and Prade, Henri and Richard, Gilles Constructive solving of Raven's IQ tests with analogical proportions. (2016) International Journal of Intelligent Systems, 31 (11). 1072-1103. ISSN 0884-8173

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Official URL: https://doi.org/10.1002/int.21817

Abstract

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 × 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.

Item Type:Article
Additional Information:https://onlinelibrary.wiley.com/doi/full/10.1002/int.21817
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
French research institutions > Institut National de la Recherche en Informatique et en Automatique - INRIA (FRANCE)
Other partners > Institut National des Sciences Appliquées de Rennes - INSA (FRANCE)
Other partners > Ecole Supérieure d'Electricité - SUPELEC (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Ecole Normale Supérieure de Rennes - ENS Rennes (FRANCE)
Other partners > IMT Atlantique Bretagne-Pays de la Loire - IMT Atlantique (FRANCE)
Other partners > Telecom Bretagne (FRANCE)
Other partners > Université de Bretagne Sud - UBS (FRANCE)
Other partners > Université de Rennes 1 (FRANCE)
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Deposited On:05 Feb 2020 08:54

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