A theoretical result [10] that relates tautological consequence in many-valued logics to the ideal membership problem in algebra is revisited. The intended use of the approach in this article and its implementation is the verification of consistency and the automated extraction of knowledge in rule-based knowledge systems. Programs are written in the CoCoA language. Four RBS are studied to illustrate the implementation.

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The aim of this paper is to present theoretically a new algebraic method for detecting potentially dangerous states in a Rule Based 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 a possible input fact such that, if it also occurred, the dangerous situation really would happen. This method, inspired by automatic discovery of geometric theorems, is based on calculating just one reduced Groebner basis of a polynomial ideal representing the system's knowledge. An implementation in the computer algebra system Maple is included.

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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. Una aproximación algebraica a los sistemas expertos basados en reglasResumen. Este artículo presenta una panorámica de la línea de investigación de los autores en extracción 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 realmenteútil para la enseñanza y para el rápido diseño de RBES.