A polynomial model for multi-valued Logics with a touch of Algebraic Geometry and Computer Algebra

Roanes–Lozano, Eugenio; Laita, Luis M.; Roanes-Macı́as, Eugenio

doi:10.1016/s0378-4754(97)00088-8

Cited by 45 publications

(17 citation statements)

References 6 publications

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“…We have to define the polynomial ring and ask CoCoA to use it: For instance, the CoCoA implementation of the polynomial expressions of a 7-valued modal logic can be found in [27]. Whether A 0 is a consequence of a set of formulae or not, can be checked with CoCoA just typing:…”

Section: Cocoa Implementationmentioning

confidence: 99%

An algebraic approach to rule based expert systems

Roanes–Lozano

Laita

Hernando

et al. 2010

Rev. R. Acad. Cien. Serie A. Mat.

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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.

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Section: Cocoa Implementationmentioning

confidence: 99%

An algebraic approach to rule based expert systems

Roanes–Lozano

Laita

Hernando

et al. 2010

Rev. R. Acad. Cien. Serie A. Mat.

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“…The logical and mathematical ideas behind the GB-based IE can be found in the mathematical model of logic and RBES in [2,3], that are based on previous works for rewriting classical Boolean [4,5] and many-valued logics [6].…”

Section: An Algebraic Model Of Rbes Whose Underlying Logic Is Classicmentioning

confidence: 99%

“…For instance, we can check that ∨ is associative (observe that this is not formally a proof: we only check it for propositional variables x [1], x [2] and x [3]; nevertheless it will also hold if x [1], x [2] and x [3] are substituted by any polynomial expressions, so it will be true in general) 9 :…”

Section: Examplementioning

confidence: 99%

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A Symbolic-Numeric Approach to MPL Continuous Logic and to Rule Based Expert Systems whose Underlying Logic is MPL

Roanes–Lozano

Laita²,

Roanes-Macı́as³

2008

TOAMJ

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Abstract:We first briefly describe an algebraic model of classical and modal many-valued logics due to the authors and introduced in previous works. A similar approach, also using Computer Algebra techniques (Gröbner bases) and oriented to perform effective calculus in a continuous logic: Minimal Polynomial Logic (MPL) is presented. The implementation has been developed in the Computer Algebra System Maple. The possibility to perform knowledge extraction and to check consistency in Rule Based Expert Systems (RBES) whose underlying logic is MPL, has also been explored. The article is illustrated with examples of very simple RBES.

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