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Interpreting Neural Networks in the Frame of the Logic of Lukasiewicz

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Connectionist Models of Neurons, Learning Processes, and Artificial Intelligence (IWANN 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2084))

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Abstract

Neural networks using a piecewise linear ramp-step activation function may be interpreted as expressions in the propositional logic of Kleene-Lukasiewicz. These expressions even though information preserving may have a high degree of complexity impairing their understandability. The paper discloses a strategy which combines classical logic with the logic of Lukasiewicz to decompose a complex rule into a set of simpler rules that cover the former.

Work leading to this paper has been partially supported by the Ministry of Education and Research, Germany, under grant BMBF-CH-99/023 and by the Technical University Federico Santa María, Chile, under grant UTFSM/DGIP-Intelligent Data Mining in Complex Systems/2000-2001.

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References

  1. Castro J. L., Trillas E.: The Logic of Neural Networks. Mathware and Softcomputing, Vol. V (1), 23–27, (1998)

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  2. Giles R.: Lukasiewicz logic and fuzzy set theory. Int. Jr. Man-Machine Studies 8, 313–327, (1976)

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  3. Trillas E.: Sobre funciones de negación en la teoría de conjuntos difusos, Stochastica III-I, 47–60, (1979)

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Author information

Authors and Affiliations

  1. Department of Computer Science, Computer Engineering and Computing Education, University of Dortmund, 44221, Dortmund, Germany

    Claudio Moraga

  2. Department of Computer Science, Technical University Federico Santa Marxía, Valparaíso, Chile

    Luis Salinas

Authors
  1. Claudio Moraga
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  2. Luis Salinas
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Editor information

Editors and Affiliations

  1. Departamento de Inteligencia Artificial Sanda del Rey, Universidad Nacional de Educación a Distancia, s/n., Madrid, 28040, Spain

    José Mira

  2. Departamento de Arquitectura y Tecnología de Computadores, Universidad de Granada, Campus Fuentenueva, 18071, Granada, Spain

    Alberto Prieto

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© 2001 Springer-Verlag Berlin Heidelberg

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Moraga, C., Salinas, L. (2001). Interpreting Neural Networks in the Frame of the Logic of Lukasiewicz. In: Mira, J., Prieto, A. (eds) Connectionist Models of Neurons, Learning Processes, and Artificial Intelligence. IWANN 2001. Lecture Notes in Computer Science, vol 2084. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45720-8_17

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  • DOI: https://doi.org/10.1007/3-540-45720-8_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42235-8

  • Online ISBN: 978-3-540-45720-6

  • eBook Packages: Springer Book Archive

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