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Article

Towards a Notion of Basis for Knowledge-Based Systems—Applications

by
Gonzalo A. Aranda-Corral
1,
Joaquín Borrego-Díaz
2,*,
Juan Galán-Páez
2 and
Daniel Rodríguez-Chavarría
2
1
Department of Information Technology, Universidad de Huelva, 21004 Huelva, Spain
2
Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, 41012 Sevilla, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2021, 9(3), 252; https://doi.org/10.3390/math9030252
Submission received: 28 December 2020 / Revised: 20 January 2021 / Accepted: 25 January 2021 / Published: 27 January 2021
(This article belongs to the Special Issue Computer Algebra and Its Applications)
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Abstract

In the paradigm of Knowledge-Based Systems (KBS), the design of methods to simplify the reasoning leads to more efficient processes. A point of view that provides valuable insights is the algebraic one. In this work, a notion of basis (and dimension) for Knowledge Bases in Propositional Logic associated with knowledge forgetting is introduced. It is based on ideas that come from the translation of such logic in (Computer) Algebra, particularly from the interpretation of variable forgetting. In this paper, the concept of weak base is defined as a set of variables sufficient to decide the consistency using variable forgetting. Several applications of weak bases are presented in order to show their usefulness in KBS reasoning and to justify their study and use in solving problems within this topic.
Keywords: knowledge-based systems; computer algebra; variable forgetting; conservative retraction knowledge-based systems; computer algebra; variable forgetting; conservative retraction

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MDPI and ACS Style

Aranda-Corral, G.A.; Borrego-Díaz, J.; Galán-Páez, J.; Rodríguez-Chavarría, D. Towards a Notion of Basis for Knowledge-Based Systems—Applications. Mathematics 2021, 9, 252. https://doi.org/10.3390/math9030252

AMA Style

Aranda-Corral GA, Borrego-Díaz J, Galán-Páez J, Rodríguez-Chavarría D. Towards a Notion of Basis for Knowledge-Based Systems—Applications. Mathematics. 2021; 9(3):252. https://doi.org/10.3390/math9030252

Chicago/Turabian Style

Aranda-Corral, Gonzalo A., Joaquín Borrego-Díaz, Juan Galán-Páez, and Daniel Rodríguez-Chavarría. 2021. "Towards a Notion of Basis for Knowledge-Based Systems—Applications" Mathematics 9, no. 3: 252. https://doi.org/10.3390/math9030252

APA Style

Aranda-Corral, G. A., Borrego-Díaz, J., Galán-Páez, J., & Rodríguez-Chavarría, D. (2021). Towards a Notion of Basis for Knowledge-Based Systems—Applications. Mathematics, 9(3), 252. https://doi.org/10.3390/math9030252

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