PRISM – Spatial Reasoning with Preferred Mental Models



Preferred Inferences in Reasoning with Spatial mental Models (PRISM) is an extension of Spatial Reasoning with mental Models (SRM) by Marco Ragni and Markus Knauff. The program can be downloaded at




The new website of the program is currently under construction. The URL is


ANN Tools for Number Series

Any mathematical pattern can be the generation principle for number series. In con-
trast to most of the application fields of artificial neural networks (ANN) a successful
solution does not only require an approximation of the underlying function but to correctly
predict the exact next number. We propose a dynamic learning approach and evaluate our
method empirically on number series from the Online Encyclopedia of Integer Sequences.
Finally, we investigate research questions about the performance of ANNs, structural prop-
erties, and the adequate architecture of the ANN to deal successfully with number series.
Solving number series poses a challenging problem for humans and Artificial Intelligence
Systems. The task is to correctly predict the next number in a given series, in accordance
with a pattern inherent to that series. We propose a novel method based on Artificial
Neural Networks with a dynamic learning approach to solve number series problems. Our
method is evaluated on an own experiment and over 50.000 number series from the Online
Encyclopedia of Integer Sequences (OEIS) database.

Raven Model

Human reasoners have an impressive ability to solve analogical reasoning problems and they still outperform computational systems. Analogical reasoning is relevant in dealing with intelligence tests. There are two kinds of approaches: to solve IQ-test problems in a way similar to humans (i.e., a cognitive approach) or to solve these problems optimally (i.e., the AI approach). Most systems can be associated with one of these approaches. Detailed systems solving geometrical intelligence tests, explaining cognitive operations based on working memory and producing precise predictions and results such as error rates and response times have not been developed so far. We present a system implemented in the cognitive architecture ACT-R, able to solve analogously developed problems of Raven’s Standard and Advanced Progressive Matrices. The model solves 66 of the 72 tested problems of both tests. The model’s predicted error rates correlate to human performance with r = .8 for the Advanced Progressive Matrices and r = .7 for all problems together.

Complexity IQ-tests

Positioning. The article, published at the European Conference on Cognitive Science, characterizes different types of problems in Cattell’s Culture Fair Test and Evan’s Analogy Problems.

Research Question. Can we classify the problems in Cattell’s Culture Fair Test, Evan’s Analogy Problems and Raven’s Matrices Tests? How good can the functional complexity measure explain the results?

Method. Formal analysis; cognitive complexity measure; empirical analysis

Results. All problem instances can be classified into three general classes of problems. A functional complexity measure, applied to Cattell’s Culture Fair Test and Evans Analogy problems, produces for the latter satisfactorily results (correctness: r = −.62, p < .01; solution time: r = -.67, p < .0001).

Ragni, M., Stahl, P., & Fangmeier, T. (2011). Cognitive Complexity in Matrix Reasoning Tasks. In B. Kokinov, A. Karmiloff-Smith, & N. J. Nersessian (Eds.), Proceedings of the European Conference on Cognitive Science. Sofia: NBU Press.

ACT-R model of IQ-tests

Positioning. The article, published at the European Conference on Artificial Intelligence 2012, presents an ACT-R model that is able to solve Raven’s Matrix Test.

Research Question. Is it possible to explain the limitations in human reasoning in IQ- tests based on working memory limitations?

Method. Cognitive modeling; formal analysis

Results. The cognitive model in ACT-R, is able to solve analogously developed problems of Raven’s Standard and Advanced Progressive Matrices. The model solves 66 of the 72 tested problems of both tests. The model’s predicted error rates correlate to human performance with r = .8 for the Advanced Progressive Matrices and r = .7 for all problems together.

Ragni, M., & Neubert, S. (2012). Solving Raven’s IQ-tests: An AI and Cognitive Modeling Approach. In L. D. Raedt et al. (Eds.), Proceedings of the 20th European Conference on Artificial Intelligence (Vol. 242, pp. 666–671). Amsterdam: IOS Press.

Complexity Analogical Reasoning

Positioning. The article, published at the European Conference on Artificial Intelligence (ECAI) in 2010, aims to capture human reasoning difficulty in Raven’s reasoning problems.

Research Question. Is it possible to introduce a complexity measure for Cattell’s Culture Fair Test problems wrt. the kind of underlying functions necessary to solve such tasks?

Method. Formal analysis and cognitive modeling.

Results. The investigations lead to the implementation of a Python program, which is able to solve matrix tasks and to evaluate their complexity by a newly developed complexity measure. The predictions of the model is compared with the human performance on solving the item’s from Cattell’s Culture Fair Test and yield to a correlation r = .72, p < .05 without weigths.

Stahl, P., & Ragni, M. (2010). Complexity in Analogy Tasks: An Analysis and Computational Model. In H. Coelho, R. Studer, & M. Wooldridge (Eds.), Proceedings of the 19th European Conference on Artificial Intelligence (Vol. 215, pp. 1041–1042). Amsterdam: IOS Press.

Dynamic Learning Approach for Solving Number Series

Positioning. The article, published as a book chapter in the Proceedings of the German Conference on Artificial Intelligence 2011, proposes to use Artificial Neural Networks to solve number series problems.

Research Question. Is it possible to develop a cognitive system able to solve number series problems of intelligence test or the 50 000 problems in the Online Encyclopedia of Integer Series?

Method. Dynamic training method for Artificial Neural Network

Results. Using a dynamic learning approach the approach can solve 26 951 of 57 524 number series.

Ragni, M., & Klein, A. (2011). Predicting numbers: An AI approach to solving number series. In S. Edelkamp & J. Bach (Eds.), KI-2011. Springer LNAI, Heidelberg.

Solving Number Series and Artificial Neural Networks

Positioning. The article, published at the International Joint Conference on Computational Intelligence (IJCI 2011), investigates if we can solve classical intelligence test problems and what parameters fit the best.

Research Question. What kind of architectural and formal properties can have an influence on successful artificial neural networks solving number series?

Method. Formal analysis of artificial neural networks

Results. Systematically testing the best parameters (number of input nodes, hidden nodes, and learning rate) shows that the structure of the Artificial Neural Networks can determine the success of solving a number sequence: 2-4 input nodes and about 5-6 hidden nodes provide the best framework to solve number series. By allowing approximations (deviations of ± 5) be improved to solve about 39 000 number series of the Online Encyclopedia.

Ragni, M., & Klein, A. (2011b). Solving Number Series – Architectural Properties of Successful Artificial Neural Networks. In K. Madani, J. Kacprzyk, & J. Filipe (Eds.), NCTA 2011 –  Proceedings of the International Conference on Neural Computation Theory and Applications(pp. 224–229). SciTePress.

Review of Complex Cognition

Positioning. The article, published in the Journal Cognitive Systems Research, presents an overview and characterization of complex cognition.

Content. Complex cognition addresses research on: “(a) high-level cognitive processes – mainly problem solving, reasoning, and decision making – and their interaction with more basic processes such as perception, learning, motivation and emotion and (b) cognitive processes which take place in a complex, typically dynamic, environment.” The article presents an overview about past and current research and a precision of the definition of complex cognition from both an AI and psychological perspective. There is a great emphasis on the challenges for cognitive systems. Complex cognition goes far beyond simple cognitive processes and requires all possible methods from cognitive science research: from analytical, empirical, to engineering methods. The article finally presents challenges for complex problem solving, dynamic decision making, and finally learning of concepts, skills and strategies.

Schmid, U., Ragni, M., Gonzalez, C., & Funke, J. (2011). The challenge of complexity for cognitive systems. Cognitive Systems Research, 12(3-4), 211-218.