Exploring set theory and logic as foundations for explainable AI and knowledge representation

Gohil, Deepali Mahesh; Puri, Ganesh Dagadu; Thanekar, Sachin Arun; Ali, Syed Sumera; Parjane, Vaibhav Arjunrao

doi:10.47974/JIM-2499

Open Access Research Article

Exploring set theory and logic as foundations for explainable AI and knowledge representation

Deepali Mahesh Gohildmgohil@dypcoeakurdi.ac.inDepartment of Computer EngineeringAkurdiD Y Patil College of EngineeringPune, Maharashtra, 411044, IndiaView full profile → , ^*Ganesh Dagadu PuriCorresponding authorpuriganeshengg@gmail.comDepartment of Computer EngineeringAmrutvahini College of EngineeringSangamner, Maharashtra, 422608, IndiaView full profile → , Sachin Arun Thanekarsachin.sangamner@gmail.comDepartment of Computer EngineeringAmrutvahini College of EngineeringSangamner, Maharashtra, 422608, IndiaView full profile → , Syed Sumera Alisyed.sumera.ali@gmail.comDepartment of Electronics & CommunicationCSMSS Chh. Shahu College of EngineeringAurangabad, Maharashtra, 431001, IndiaView full profile → , Vaibhav Arjunrao Parjaneparjanevaibhav77@gmail.com vaparjanecm@sanjivani.org.inDepartment of Computer TechnologySanjivani K.B.P. PolytechnicKopargaon, Maharashtra, 423603, IndiaView full profile →

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pp. 645–653Vol. 29Issue 3March 2026DOI: 10.47974/JIM-2499XML

Received:: 01 Mar 2025
Published Online:: 18 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2499
Pages:: 645–653

Abstract

In this research study, the importance of set theory and logic as the building blocks of artificial intelligence (AI) that can be explained and the representation of knowledge are examined. We render AI more understandable through formalization of knowledge with the help of set-theoretical and logical schemes. The research examines the roles played by the use of the space of vectors, orthogonal sets and sequences in a manner that streamlines knowledge bases in a manner that is mathematically sound. It further demonstrates the importance of logical reasoning methods in making decision-making processes of AI systems transparent, which is significant standards of explainability. By integrating AI models in such a manner, they will be simpler to comprehend, more credible, and will address complex issues more efficiently.

Keywords

Set theory Logic Explainable AI Knowledge representation Logical inference

Subject Classifications

03E15

References

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