Deductive Reasoning - Using Artificial Neural Networks to Simulate Preferential Reasoning

Marco Ragni, Andreas Klein

Abstract

Composition tables are used in AI for knowledge representation and to compute transitive inferences. Most of these tables are computed by hand, i.e., there is the need to generate them automatically. Furthermore, human preferred solutions and errors in reasoning can be explained as well based on these tables. First, we will report briefly psychological results about the preferences in calculi. Then we show that we can train ANNs on a simple calculus like the point algebra and the trained ANN is able to correctly solve larger calculi such as the Cardinal Direction Calculus. As human prefer specific conclusions, we are able to show that based on the ANN, which is trained on the preferred conclusions of the point algebra alone, is able to reproduce the results on the larger calculi as well. Finally, we show that humans preferred solutions can be adequately described by the networks. A brief discussion of the structure of successful ANNs conclude the paper.

References

  1. Bennett, B., Isli, A., and Cohn, A. G. (1997). When does a composition table provide a complete and tractable proof procedure for a relational constraint language? In Proceedings of the IJCAI97 Workshop on Spatial and Temporal Reasoning, Nagoya, Japan.
  2. Cohn, A. G. (1997). Qualitative spatial representation and reasoning techniques. In Brewka, G., Habel, C., and Nebel, B., editors, KI-97: Advances in Artificial Intelligence, Berlin, Germany. Springer-Verlag.
  3. Franco, L. (2006). Generalization ability of boolean functions implemented in feedforward neural networks. Neurocomputing, 70:351-361.
  4. Ragni, M. and Becker, B. (2010). Preferences in cardinal direction. In Ohlsson, S. and Catrambone, R., editors, Proc. of the 32nd Cognitive Science Conference, pages 660-666, Austin, TX.
  5. Rauh, R., Hagen, C., Knauff, M., Kuss, T., Schlieder, C., and Strube, G. (2005). Preferred and Alternative Mental Models in Spatial Reasoning. Spatial Cognition and Computation, 5.
Download


Paper Citation


in Harvard Style

Ragni M. and Klein A. (2012). Deductive Reasoning - Using Artificial Neural Networks to Simulate Preferential Reasoning . In Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: NCTA, (IJCCI 2012) ISBN 978-989-8565-33-4, pages 635-638. DOI: 10.5220/0004155106350638


in Bibtex Style

@conference{ncta12,
author={Marco Ragni and Andreas Klein},
title={Deductive Reasoning - Using Artificial Neural Networks to Simulate Preferential Reasoning},
booktitle={Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: NCTA, (IJCCI 2012)},
year={2012},
pages={635-638},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004155106350638},
isbn={978-989-8565-33-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: NCTA, (IJCCI 2012)
TI - Deductive Reasoning - Using Artificial Neural Networks to Simulate Preferential Reasoning
SN - 978-989-8565-33-4
AU - Ragni M.
AU - Klein A.
PY - 2012
SP - 635
EP - 638
DO - 10.5220/0004155106350638