An interpretation of the propositional Boolean algebra as a k-algebra. Effective calculus

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

doi:10.1007/3-540-60156-2_18

Cited by 10 publications

(5 citation statements)

References 4 publications

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“…Definition 18 We shall say that there is strong inconsistency if and only if the conjunction of the facts in a certain consistent set of facts, the rules and the negations of integrity constraints of the RBES, can only take the truth value "false".…”

Section: Rbes Strong and Weak Inconsistency Algebraic Interpretationmentioning

confidence: 99%

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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: Rbes Strong and Weak Inconsistency Algebraic Interpretationmentioning

confidence: 99%

“…The proofs omitted in this section can be found in [18,28] (these references also extend both Sections 3 and 4). For a deeper study of Boolean algebras see, for instance, [10,11,12,22,36].…”

Section: An Introduction To Boolean Algebras and Boolean Ringsmentioning

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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“…A polynomial model for propositional Boolean algebras (a residue class ring) was shown in [12]. This model was adapted to check the consistency of Knowledge Based Systems (KBSs) based on classical bivalued logic, by moving to the residue class ring over another ideal [20][21][22].…”

Section: Introductionmentioning

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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“…Indeed, as may be seen in[14,19,20], there are many deep relations between algebraic structures and propositional logic.…”

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confidence: 97%

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

Roanes–Lozano

Hernando

Laita

et al. 2009

Ann Math Artif Intell

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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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An interpretation of the propositional Boolean algebra as a k-algebra. Effective calculus

Cited by 10 publications

References 4 publications

An algebraic approach to rule based expert systems

An algebraic approach to rule based expert systems

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

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

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