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An algebraic approach for detecting nearly dangerous situations in expert systems

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  • Maestre-Martínez, Roberto
  • Hernando, Antonio
  • Roanes-Lozano, Eugenio

Abstract

The aim of this work is to present theoretically a new algebraic method for detecting nearly dangerous states in an expert system whose knowledge is represented by propositional Boolean logic. Given a dangerous state which does not happen at present, our method is able to detect if a dangerous situation would happen if an input variable of the Expert System changed. The method presented here is based on calculating just one Groebner basis of a polynomial ideal representing the system knowledge. In this way, although the Expert System is designed to notify only dangerous situations, we have developed an algebraic model for including in the expert system the ability to recommend watching carefully some Boolean variables such that if one of them changed, the system would fall in a dangerous situation. In this way, the same expert system not only warns about dangerous situations but also about nearly dangerous situations. It may be noted that our method does not require to change the Expert System for including this facility. As far as our knowledge goes, our work is completely new in the field of Expert Systems.

Suggested Citation

  • Maestre-Martínez, Roberto & Hernando, Antonio & Roanes-Lozano, Eugenio, 2016. "An algebraic approach for detecting nearly dangerous situations in expert systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 129(C), pages 81-93.
    • Handle: RePEc:eee:matcom:v:129:y:2016:i:c:p:81-93
    DOI: 10.1016/j.matcom.2016.04.001
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    References listed on IDEAS

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    1. Hernando, Antonio & Roanes-Lozano, Eugenio, 2015. "An algebraic model for implementing expert systems based on the knowledge of different experts," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 107(C), pages 92-107.
    2. Pérez-Carretero, Cristina & Laita, Luis M. & Roanes-Lozano, Eugenio & Lázaro, Luis & González-Cajal, Jesús & Laita, Laura, 2002. "A logic and computer algebra-based expert system for diagnosis of anorexia," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(3), pages 183-202.
    3. Hernando, Antonio, 2011. "A new algebraic model for implementing expert systems represented under the ‘Concept-Attribute-Value’ paradigm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(1), pages 29-43.
    4. Roanes-Lozano, Eugenio & Hernando, Antonio & Alonso, Jose Antonio & Laita, Luis M., 2011. "A logic approach to decision taking in a railway interlocking system using Maple," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(1), pages 15-28.
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