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An algebraic approach to rule based expert systems

Una aproximación algebraica a los sistemas expertos basados en reglas

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Abstract

This article presents a survey of the authors' research on knowledge extraction and verification of Rule Based Expert Systems (RBES) using algebraic inference engines and based on Gröbner bases theory. A shell, including a graphic user interface and inference engines for different logics (both classic and modal multi-valued) as well as in different computer algebra systems, is also presented here. The shell distinguishes three levels: at the lower level, we provIDe the computer algebra system code of the algebraic inference engines; at the intermediate level, the RBES developer has to detail the rules and integrity constraints of a certain RBES; and, finally, at the upper level, the final user deals with a simple GUI, where he can perform knowledge extraction or verify the RBES, after choosing the logic and inputing a consistent set of facts. We believe that this shell can be really useful for teaching and quick RBES design.

Resumen

Este artículo presenta una panorámica de la línea de investigación de los autores en extracci ón de conocimiento y verificación de Sistemas Expertos Basados en Reglas (RBES) usando motores de inferencia algebraicos y basada en la teoría de bases de Gröbner. Se presenta también una shell, que incluye una interfaz gráfica de usuario y motores de inferencia para distintas lógicas (tanto clásicas como modales multivaluadas) y en distintos sistemas de cómputo algebraico. La shell distingue tres niveles: en el más bajo proporcionamos el código del motor de inferencia para el sistema de cómputo algebraico elegIDo; en el intermedio el desarrollador del RBES tiene que detallar las reglas y las restricciones de integrIDad de un cierto RBES; y, finalmente, en el nivel superior, el usuario final trata con una sencilla interfaz gráfica de usuario, en la que puede llevar a cabo extracción de conocimiento o verificar el RBES, después de elegir la lógica y de introducir un conjunto consistente de hechos. Creemos que esta shell puede ser realmente útil para la enseñanza y para el rápIDo diseño de RBES.

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Authors and Affiliations

  1. Depto. de Álgebra Facultad de Educación, UniversIDad Complutense de MadrID, c/ Rector Royo Villanova s/n, 28040, MadrID, Spain

    Eugenio Roanes-Lozano & Eugenio Roanes-Macías

  2. Depto. de Sistemas Inteligentes Aplicados Escuela Universitaria de Informática, UniversIDad Politécnica de MadrID, Carretera de Valencia km 7, 28031, MadrID, Spain

    Antonio Hernando

  3. Depto. CC. de la Computacioń e I.A. Facultad de Informática, UniversIDad Politécnica de MadrID, Campus de Montegancedo Boadilla del Monte, 28660, MadrID, Spain

    Luis M. Laita

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  1. Eugenio Roanes-Lozano
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  2. Luis M. Laita
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  3. Antonio Hernando
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  4. Eugenio Roanes-Macías
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Correspondence to Eugenio Roanes-Lozano.

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Submitted by DavID Ríos Insua.

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Roanes-Lozano, E., Laita, L.M., Hernando, A. et al. An algebraic approach to rule based expert systems. Rev. R. Acad. Cien. Serie A. Mat. 104, 19–40 (2010). https://doi.org/10.5052/RACSAM.2010.04

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