Reasoning

A central aspect of intelligence, be it natural or artificial is the ability to reason about given information and to solve problems. Reasoning is the ability to gain new information from existing knowledge and is among the most basic human cognitive abilities and a central issue in current psychological research. Reasoning can be deductively, inductively or abductively. The following investigations contribute to all three parts within the classical distinction: syllogistic reasoning, conditional reasoning, and relational reasoning.

Papers:

Programs:

  • Reasoning with IQ tasks:
    • Solver IQ Tasks: The program allows the user to design arbitrary geometrical tasks like such used in the Raven or CFT3 intelligence tests. The tasks are solved by the program and their complexity for human subjects is evaluated. The complexity measure is based on an analysis of the empricial data from the CFT3.
    • Web experiment: types of geometrical problems
    • The website IQCoach.de offers a huge database of geometrical problems which are similar to such used in intelligence tests. Users of the website can train their problem solving strategies by performing different types of task and tests. All tasks are generated according to a database of different problem principles, which were collected from an analysis of different tests in the literature. All tasks are characterized according to their problem structure and stimuli. This allows users to train individually specific types of tasks.
      The website was realized by a Karl Steinbuch scholarship.
    • 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.
  • Reasoning with mental models
    • SRM with negations
    • SRM with boolean and syllogistic reasoning
    • 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.
  • Solving Number Series: ANN learning tools – Any mathematical pattern can be the generation principle for number series. In contrast 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 properties, 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.