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

• Main Authors: Gonzalo A. Aranda-Corral, Joaquín Borrego-Díaz, Juan Galán-Páez, Daniel Rodríguez-Chavarría
• Format: Article
• Language: English
• Published: MDPI AG 2021-01-01
• Series: Mathematics
• Subjects: knowledge-based systems; computer algebra; variable forgetting; conservative retraction
• Online Access: https://www.mdpi.com/2227-7390/9/3/252

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 <i>variable forgetting</i>. In this paper, the concept of <i>weak base</i> 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.