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Towards a Notion of Basis for Knowledge-Based Systems—Applications

Author

Listed:
  • Gonzalo A. Aranda-Corral

    (Department of Information Technology, Universidad de Huelva, 21004 Huelva, Spain)

  • Joaquín Borrego-Díaz

    (Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, 41012 Sevilla, Spain)

  • Juan Galán-Páez

    (Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, 41012 Sevilla, Spain)

  • Daniel Rodríguez-Chavarría

    (Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, 41012 Sevilla, Spain)

Abstract

In the paradigm of Knowledge-Based Systems (KBS), the design of methods to simplify the reasoning leads to more efficient processes. A point of view that provides valuable insights is the algebraic one. In this work, a notion of basis (and dimension) for Knowledge Bases in Propositional Logic associated with knowledge forgetting is introduced. It is based on ideas that come from the translation of such logic in (Computer) Algebra, particularly from the interpretation of variable forgetting . In this paper, the concept of weak base is defined as a set of variables sufficient to decide the consistency using variable forgetting. Several applications of weak bases are presented in order to show their usefulness in KBS reasoning and to justify their study and use in solving problems within this topic.

Suggested Citation

  • Gonzalo A. Aranda-Corral & Joaquín Borrego-Díaz & Juan Galán-Páez & Daniel Rodríguez-Chavarría, 2021. "Towards a Notion of Basis for Knowledge-Based Systems—Applications," Mathematics, MDPI, vol. 9(3), pages 1-22, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:252-:d:488230
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    References listed on IDEAS

    as
    1. Roanes-Lozano, Eugenio & Galán-García, José Luis & Aguilera-Venegas, Gabriel, 2015. "A portable knowledge-based system for car breakdown evaluation," Applied Mathematics and Computation, Elsevier, vol. 267(C), pages 758-770.
    2. Roanes-Lozano, Eugenio & Galán-García, José Luis & Aguilera-Venegas, Gabriel, 2017. "A prototype of a RBES for personalized menus generation," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 615-624.
    3. 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.
    4. Antonio Hernando & Roberto Maestre & Eugenio Roanes-Lozano, 2018. "A New Algebraic Approach to Decision Making in a Railway Interlocking System Based on Preprocess," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-14, October.
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