A novel way to build expert systems with infinite-valued attributes

Antonio Hernando; José Luis Galán-García; Gabriel Aguilera-Venegas; Antonio Hernando; José Luis Galán-García; Gabriel Aguilera-Venegas

doi:10.3934/math.2024145

AIMS Mathematics

2024, Volume 9, Issue 2: 2938-2963. doi: 10.3934/math.2024145

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A novel way to build expert systems with infinite-valued attributes

1.
Depto. de Sistemas Informáticos, E.T.S.I. de Sistemas Informáticos, Universidad Politécnica de Madrid, Madrid, Spain
2.
Departamento de Matemática Aplicada, Escuela de Ingenierías Industriales, Universidad de Málaga, Málaga, Spain

Received: 20 October 2023 Revised: 19 December 2023 Accepted: 27 December 2023 Published: 02 January 2024

An expert system is a computer program that uses the knowledge of an expert to solve problems in a specific domain. Expert systems are used in a wide variety of fields, such as medicine, financial diagnosis and engineering. The attributes of an expert system are the characteristics of the problems that the system can solve. In traditional expert systems, attributes typically have a finite number of possible values. However, in scenarios where an attribute can assume a value from an infinite (or significantly large finite) set, the expert system cannot be represented using propositional logic. Until now, no method had been identified to implement such a system on a Computer Algebra System. Here, we break new ground by presenting a model that not only addresses this gap but also provides a fresh perspective on previous results. In fact, these prior results can be viewed as specific instances within the broader framework of our proposed solution. In this paper, we put forth an algebraic approach for the development of expert systems capable of handling attributes with infinite values, thereby expanding the problem-solving capacity of these systems.
- Gröbner bases,
- logic and symbolic computing,
- rule based expert systems
Citation: Antonio Hernando, José Luis Galán-García, Gabriel Aguilera-Venegas. A novel way to build expert systems with infinite-valued attributes[J]. AIMS Mathematics, 2024, 9(2): 2938-2963. doi: 10.3934/math.2024145

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Abstract

An expert system is a computer program that uses the knowledge of an expert to solve problems in a specific domain. Expert systems are used in a wide variety of fields, such as medicine, financial diagnosis and engineering. The attributes of an expert system are the characteristics of the problems that the system can solve. In traditional expert systems, attributes typically have a finite number of possible values. However, in scenarios where an attribute can assume a value from an infinite (or significantly large finite) set, the expert system cannot be represented using propositional logic. Until now, no method had been identified to implement such a system on a Computer Algebra System. Here, we break new ground by presenting a model that not only addresses this gap but also provides a fresh perspective on previous results. In fact, these prior results can be viewed as specific instances within the broader framework of our proposed solution. In this paper, we put forth an algebraic approach for the development of expert systems capable of handling attributes with infinite values, thereby expanding the problem-solving capacity of these systems.

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