A Groebner bases-based approach to backward reasoning in rule based expert systems

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

doi:10.1007/s10472-009-9147-4

Cited by 10 publications

(10 citation statements)

References 18 publications

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“…In [6] authors show an algebraic method for detecting potentially dangerous states in a Rule Based Expert System (RBES) whose knowledge is represented by Propositional Logic. Given K made up of rules, the idea is to consider the potential facts that make K to infer an unwanted value (which leads a danger or undesirable state).…”

Section: Detecting Potentially Dangerous Statesmentioning

confidence: 99%

A logic-algebraic tool for reasoning with Knowledge-Based Systems

Alonso-Jiménez¹,

Aranda-Corral²,

Borrego-Díaz³

et al. 2018

Journal of Logical and Algebraic Methods in Programming

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A detailed exposition of foundations of a logic-algebraic model for reasoning with knowledge bases specified by propositional (Boolean) logic is presented. The model is conceived from the logical translation of usual derivatives on polynomials (on residue rings) which is used to design a new inference rule of algebro-geometric inspiration. Soundness and (refutational) completeness of the rule are proved. Some applications of the tools introduced in the paper are shown.

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Section: Detecting Potentially Dangerous Statesmentioning

confidence: 99%

A logic-algebraic tool for reasoning with Knowledge-Based Systems

Alonso-Jiménez¹,

Aranda-Corral²,

Borrego-Díaz³

et al. 2018

Journal of Logical and Algebraic Methods in Programming

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“…The model described in [24] has been widely used to implement different expert systems using mathematical software like CoCoA or Maple. These computational algebra-based expert systems can be very easily implemented and present the advantage of enabling very quick deductions once the reduced Groebner basis is calculated [25].…”

Section: Possible Applicationsmentioning

confidence: 99%

A Polynomial Model for Logics with a Prime Power Number of Truth Values

2010

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This paper is concerned with a polynomial model (residue class ring) for a given q-valued propositional logic (where q is a power of a prime integer). This model allows to transfer logic problems into algebraic terms, resulting in an immediate computational approach to Knowledge Based Systems based on multi-valued logics. By means of this new approach, we have extended an already existent algebraic model to logics with a prime power number of truth values, while also getting more straightforward proofs and a more direct enunciation of the central theorem of this model.

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“…Details on the topic of this section, our most recent result, can be found in [25]. Based on the classical works of automatic discovery of geometric theorems [14,23] (a topic already advanced in [8]), we have now adapted this idea to a specific task in RBES whose underlying logic is classic Boolean logic: given a set of facts and a goal, finding a new fact such that if it also held, this goal would be inferred.…”

Section: Backward Reasoning In Rule Based Expert Systems Whose Underlmentioning

confidence: 99%

“…Based on the classical works of automatic discovery of geometric theorems [14,23] (a topic already advanced in [8]), we have now adapted this idea to a specific task in RBES whose underlying logic is classic Boolean logic: given a set of facts and a goal, finding a new fact such that if it also held, this goal would be inferred. The main result proven in [25] (Theorem 5 below) shows how it is enough to compute one single reduced GB in order to detect them:…”

Section: Backward Reasoning In Rule Based Expert Systems Whose Underlmentioning

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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A Groebner bases-based approach to backward reasoning in rule based expert systems

Cited by 10 publications

References 18 publications

A logic-algebraic tool for reasoning with Knowledge-Based Systems

A logic-algebraic tool for reasoning with Knowledge-Based Systems

A Polynomial Model for Logics with a Prime Power Number of Truth Values

An algebraic approach to rule based expert systems

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