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Galoitica: Journal of Mathematical Structures and Applications

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Galoitica: Journal of Mathematical Structures and Applications
Full Length Article

Volume 13Issue 2PP: 01–05 • 2026

Turiyam Set Comparison with Aristotle and Belnap Four-Valued Logic

Prem Kumar Singh 1*
1Department of Computer Science and Engineering, Gandhi Institute of Technology and Management, Visakhapatnam, Andhra Pradesh 530045, India
* Corresponding Author.
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© 2026 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: November 02, 2025 Revised: December 28, 2025 Accepted: January 27, 2026

Abstract

In recent times, investigating data with Turiyam attributes and its analysis has been considered one of the crucial tasks. It provides a way to characterize fuzziness in attributes in four independent ways: the true region (t), false region ( f ), indeterminate region (i), and liberal region (l). Numerous algorithms have been suggested for applications of the Turiyam set as a graph, a Turiyam matrix and algebraic properties of a Turiyam matrix. It tries to use words to calculate whenever there’s a human consciousness. One suitable example is the voting system in a democratic country like India where people vote according to their conduit metaphor or they select NOTA. There are, however, several older four valued methods, such as those of Nagarjuna (Catuskoti) and Aristotle’s logic and Belnap’s logic. The author gives an example to compare the Turiyam logic with each of these approaches in this paper.

Keywords

Aristotle logic Anekantavada Consciousness Four-valued logic Unknown Turiyam set

References

[1] P. K. Singh, “Data with Turiyam set for fourthdimension quantum information processing,” Journal of Neutrosophic and Fuzzy Systems, vol. 1, no. 1, pp. 9–23, 2021.

[2] P. K. Singh, N. Surathu, and G. S. Prakash, “Turiyambased four-way unknown profile characterization on social networks,” Journal of Galoitica: Journal of Mathematical Structures and Applications, vol. 10, no. 2, pp. 27–43, 2024.

[3] S., “Four-dimensional space,” Nature, vol. 31, p. 481, [4] T. Parsons and G. Ciola, “The traditional square of opposition,” 1997.

[5] S. Boffa and P. Murinova, “Aristotle’s square for mining fuzzy concepts,” Fuzzy Sets and Systems, vol. 508, p. 109323, 2025.

[6] N. D. Belnap, “A useful four-valued logic,” in Modern Uses of Multiple-Valued Logic: Proceedings of the Fifth International Symposium on Multiple-Valued Logic, J. M. Dunn and G. Epstein, Eds. D. Reidel Publishing Company, 1975, pp. 8–37.

[7] G. I. Gurdjieff, In Search of Being: The Fourth Way to Consciousness. Shambhala Publications, 2021.

[8] P. D. Ouspensky, A New Model of the Universe. New York: Vintage Books, 1971, p. 378.

[9] P. C. Mahalanobis, “The Indian-Jaina dialectic of Syadvad in relation to probability (i),” Dialectica, vol. 8, pp. 95–111, 1954.

[10] G. B. Burch, “Seven-valued logic in Jain philosophy,” International Philosophical Quarterly, vol. 4, no. 1, pp. 68–93, 1964.

[11] A. Schumann, “Nagarjunian-Yogacarian modal logic versus Aristotelian modal logic,” Journal of Indian Philosophy, vol. 49, pp. 467–498, 2021.

[12] N. Martin, R. Priya, P. K. Singh, and R. Gandhi, “Turiyam cognitive maps in optimal industrial decision making,” Big Data and Computing Visions, vol. 5, no. 4, pp. 276–286, 2025.

Cite This Article

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Singh, Prem Kumar. "Turiyam Set Comparison with Aristotle and Belnap Four-Valued Logic." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 13, no. Issue 2, 2026, pp. 01–05. DOI: https://doi.org/10.54216/GJMSA.130201
Singh, P. (2026). Turiyam Set Comparison with Aristotle and Belnap Four-Valued Logic. Galoitica: Journal of Mathematical Structures and Applications, Volume 13(Issue 2), 01–05. DOI: https://doi.org/10.54216/GJMSA.130201
Singh, Prem Kumar. "Turiyam Set Comparison with Aristotle and Belnap Four-Valued Logic." Galoitica: Journal of Mathematical Structures and Applications Volume 13, no. Issue 2 (2026): 01–05. DOI: https://doi.org/10.54216/GJMSA.130201
Singh, P. (2026) 'Turiyam Set Comparison with Aristotle and Belnap Four-Valued Logic', Galoitica: Journal of Mathematical Structures and Applications, Volume 13(Issue 2), pp. 01–05. DOI: https://doi.org/10.54216/GJMSA.130201
Singh P. Turiyam Set Comparison with Aristotle and Belnap Four-Valued Logic. Galoitica: Journal of Mathematical Structures and Applications. 2026;Volume 13(Issue 2):01–05. DOI: https://doi.org/10.54216/GJMSA.130201
P. Singh, "Turiyam Set Comparison with Aristotle and Belnap Four-Valued Logic," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 13, no. Issue 2, pp. 01–05, 2026. DOI: https://doi.org/10.54216/GJMSA.130201
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