Set theory and logic-driven AI reasoning for decision-making systems

Mane, Pravin; Kaur, Dalwinder; Badhiye, Sagarkumar S.; Panhalkar, Archana R.; Ashirova, Anorgul

doi:10.47974/JIM-2502

Open Access Research Article

Set theory and logic-driven AI reasoning for decision-making systems

Pravin Manepravin.mane@bharatividyapeeth.eduDepartment of Management StudiesBharati Vidyapeeth (Deemed to be University)Institute of Management and Entrepreneurship Development PunePune, Maharashtra, 411038, IndiaView full profile → , Dalwinder Kaurdalvyndhillon@gmail.comSchool of EducationNo. 3 Jalan Kia PengManipal GlobalNxt UniversityKuala Lumpur, 50450, MalaysiaView full profile → , ^*Sagarkumar S. BadhiyeCorresponding authorsagarbadhiye@gmail.comDepartment of Computer Science and EngineeringNagpur Campus, Symbiosis International (Deemed University)Symbiosis Institute of TechnologyNagpur, Maharashtra, 440008, IndiaView full profile → , Archana R. Panhalkararchana10bhosale@rediffmail.comDepartment of Artificial Intelligence and Data ScienceAmrutvahini College of EngineeringSangamner, Maharashtra, 422608, IndiaView full profile → , Anorgul Ashirovaashirova_anorgul@mamunedu.uzDepartment of General Professional SciencesMamun UniversityKhiva, 220900, Uzbekistan0000-0002-3399-7527View full profile →

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pp. 671–679Vol. 29Issue 3March 2026DOI: 10.47974/JIM-2502XML

Received:: 01 Apr 2025
Published Online:: 18 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2502
Pages:: 671–679

Abstract

In the systems making decisions, this paper examines the ability of set theory and logic to be combined as building blocks to AI-driven thinking. It is revealed that modeling any complex decision problem become clear and structured through the formalization of the knowledge representation by sets and logical formulae. Application of propositional and predicate logic allows strong reasoning processes to arrive at good results and assist individuals to make good decisions. In this case we demonstrate how to construct decision-making systems in a manner that represents them as logical and set-based structures. This approach offers a systematic and scientifically valid approach to the development of decision-support systems that are effective, easy to comprehend, and straightforward.

Keywords

Set theory Logical inference Knowledge representation Decision-making systems Propositional logic Predicate logic

Subject Classifications

03E0503E75

References

[1] Z. Wan, C. K. Liu, H. Yang, C. Li, H. You, Y. Fu, C. Wan, T. Krishna, Y. Lin, and A. Raychowdhury, “Towards Cognitive AI Systems: A Survey and Prospective on Neuro-Symbolic AI,” arXiv preprint, arXiv:2401.01040 (2024).
[2] Zhong-Zhi Li, Duzhen Zhang, Ming-Liang Zhang, Jiaxin Zhang, Zengyan Liu, Yuxuan Yao, Haotian Xu, and Junhao Zheng, “From System 1 to System 2: A Survey of Reasoning Large Language Models,” arXiv preprint, arXiv:2502.17419 (2025).
[3] Timo Schick, Jane Dwivedi-Yu, Roberto Dessì, Roberta Raileanu, Maria Lomeli, Luke Zettlemoyer, Nicola Cancedda, and Thomas Scialom, “Toolformer: Language models can teach themselves to use tools,” Advances in Neural Information Processing Systems, vol. 36, pp. 68539–68551 (2023).
[4] Omar Khattab, Arnav Singhvi, Paridhi Maheshwari, Zhiyuan Zhang, and Keshav Santhanam, “Dspy: Compiling declarative language model calls into self-improving pipelines,” arXiv preprint, arXiv:2310.03714, 2023).
[5] P. Chiranjeevi, T. Poojitha, R. N. Hemanth Kumar, A. B. Sameer, and B. Sai Dharma Teja, “CodeMate: A coding chatbot using generative AI,” International Journal for Interdisciplinary Sciences and Engineering Applications (IJISEA), vol. 6, no. 2, pp. 60–65 (2025).
[6] S. S. Patil and E. Rosemaro, “Automated Cyber Threat Intelligence Analysis using Machine Learning,” International Journal of Advanced Computer Engineering and Communication Technology (IJACECT), vol. 12, no. 1, pp. 11–17 (Apr. 2025).
[7] S. J. Purgał, D. M. Cerna, and C. Kaliszyk, “Differentiable inductive logic programming in high-dimensional space,” arXiv preprint, arXiv:2208.06652, 2022).
[8] K. Gao, K. Inoue, Y. Cao, and H. Wang, “Learning first-order rules with differentiable logic program semantics,” arXiv preprint, arXiv:2204.13570 (2022).
[9] H. Shindo, M. Nishino, and A. Yamamoto, “Differentiable inductive logic programming for structured examples,” in Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, pp. 5034–5041 (2021).
[10] B. M. Sulaiman, B. A. Hassan, and R. M. Sulaiman, “A new secant method for minima one variable problems,” Journal of Interdisciplinary Mathematics, vol. 26, no. 6, pp. 1015–1021 (2023).
[11] Matthieu Zimmer, Xuening Feng, Claire Glanois, Zhaohui Jiang, Jianyi Zhang, Paul Weng, Dong Li, Jianye Hao and Wulong Liu, “Differentiable logic machines,” arXiv preprint, arXiv:2102.11529 (2021).
[12] H. Shindo, V. Pfanschilling, D. S. Dhami, and K. Kersting, “Learning differentiable logic programs for abstract visual reasoning,” Machine Learning, vol. 113, pp. 8533–8584 (2024).
[13] D. Dhabliya, A. Lavhale, S. Thakur, R. M. Gomathi, A. Kumar, and S. De, “Enhancing cryptographic security through zero-knowledge proofs in theoretical mathematics,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 2-B, pp. 913–921 (2026), doi: 10.47974/JDMSC-2542.
[14] A. K. Rajpoot, D. Dhabliya, V. N. Trupti, T. A. Wani, K. Gupta, and L. Lakshmanan, “Quantum cryptography assessing the security and practicality of quantum key distribution in modern communication networks,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 2-B, pp. 979–986 (2026), doi: 10.47974/JDMSC-2549.
[15] P. Sahane, M. Gulhane, N. Rakesh, S. M. M. Naidu, M. Grover, and V. Mahajan, “Evaluating lightweight encryption schemes for resource-constrained devices in wireless sensor networks,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 28, no. 5-A, pp. 1803–1812 (2025), doi: 10.47974/JDMSC-2180.

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