1
University of New Mexico, Dept. Mathematics, Physics and Natural Sciences 705 Gurley Ave., Gallup, NM 87301, USA
(smarand@unm.edu)
2
Malang Institute of Agriculture, East Java, Indonesia
(victorchristianto@gmail.com)
Abstract :
The present article delves into the extension of Knuth’s fundamental Boolean logic table to accommodate the complexities of indeterminate truth values through the integration of neutrosophic logic (Smarandache & Christianto, 2008). Neutrosophic logic, rooted in Florentin Smarandache’s groundbreaking work on Neutrosophic Logic (cf. Smarandache, 2005, and his other works), introduces an additional truth value, ‘indeterminate,’ enabling a more comprehensive framework to analyze uncertainties inherent in computational systems. By bridging the gap between traditional boolean operations and the indeterminacy present in various real-world scenarios, this extension redefines logic tables, introducing neutrosophic operators that capture nuances beyond the binary realm. Through a thorough exploration of neutrosophic logic's principles and its implications in computational paradigms, this study proposes a novel approach to logic design that accommodates uncertain, imprecise, and incomplete information. This paradigm shift in logic tables not only broadens the spectrum of computing methodologies but also holds promise in fields such as decision-making systems and data analytics. This article amalgamates insights from over twelve key references encompassing seminal works in boolean logic, neutrosophic logic, and their applications in diverse scientific and computational domains, aiming to pave the way for a more robust and adaptable logic framework in computation.
Keywords :
Knuth’s Boolean logic table; Neutrosophic logic table; Neutrosophic Logic; uncertainties inherent in computational systems; adaptable logic framework.
References :
[1] Aczel, P. (1966). Lectures on Functional Equations and Their Applications. Dover Publications.
[2] Atanassov, K. T. (2019). Intuitionistic Fuzzy Sets: Theory and Applications. Springer.
[3] Hong, D. H., & Kim, M. H. (2016). Neutrosophic logic and its applications. Information Sciences, 324, 208-229.
[4] Knuth, D. E. (1997). The Art of Computer Programming, Vol. 1: Fundamental Algorithms (3rd ed.). Addison-Wesley Professional.
[5] Liu, P., & Luo, X. (2020). A Comprehensive Survey of Neutrosophic Sets: From Theoretical Foundations to Practical Applications. IEEE Access, 8, 50801-50825.
[6] Nielsen, M.A. & I.L. Chuang ( ) Quantum Computation and Quantum Information. Cambridge: Cambridge University Press.
[7] Smarandache, F. (2005). A Unifying Field in Logics: Neutrosophic Logic. Multiple-Valued Logic, 10, 289-371.
[8] Smarandache, F. (2015). Symbolic Neutrosophic Theory. Bruxelles: Europa Nova asbl . ISBN: 978-1- 59973-375-3. url: https://fs.unm.edu/SymbolicNeutrosophicTheory.pdf
[9] Smarandache F., & V. Christianto (2008) n-ary Fuzzy Logic and Neutrosophic Logic Operators, Studies in Logic, Grammar and Rethoric [Belarus], 17 (30), pp. 1-16, 2009,https://arxiv.org/abs/0808.3109 ; DOI :https://doi.org/10.48550/arXiv.0808.3109
[10] Smarandache, F., & Dezert, J. (2004). Advancements of Neutrosophic Logic: Theory and Applications. Aalborg University Press.
[11] Szpankowski, W. (2003) Average Case Analysis of Algorithms on Sequences. Dept. Computer Science, Purdue University, USA.
[12] Wang, H., & Smarandache, F. (2015). Neutrosophic Logic: A Unifying Field in Logics. Hexis.
[13] Wang, J., & Zhang, H. (2017). Generalized Neutrosophic Sets and Their Application in Multi-criteria Decision-making. Springer.
[14] Ye, J. (2019). Neutrosophic logic and its applications in information fusion. Information Fusion, 48, 32- 40.
| Style | # |
|---|---|
| MLA | Florentin Smarandache, Victor Christianto. "A few little steps beyond Knuth’s Boolean Logic Table with Neutrosophic Logic: A Paradigm Shift in Uncertain Computation." Prospects for Applied Mathematics and Data Analysis, Vol. 2, No. 2, 2023 ,PP. 22-26 (Doi : https://doi.org/10.54216/PAMDA.020201) |
| APA | Florentin Smarandache, Victor Christianto. (2023). A few little steps beyond Knuth’s Boolean Logic Table with Neutrosophic Logic: A Paradigm Shift in Uncertain Computation. Journal of Prospects for Applied Mathematics and Data Analysis, 2 ( 2 ), 22-26 (Doi : https://doi.org/10.54216/PAMDA.020201) |
| Chicago | Florentin Smarandache, Victor Christianto. "A few little steps beyond Knuth’s Boolean Logic Table with Neutrosophic Logic: A Paradigm Shift in Uncertain Computation." Journal of Prospects for Applied Mathematics and Data Analysis, 2 no. 2 (2023): 22-26 (Doi : https://doi.org/10.54216/PAMDA.020201) |
| Harvard | Florentin Smarandache, Victor Christianto. (2023). A few little steps beyond Knuth’s Boolean Logic Table with Neutrosophic Logic: A Paradigm Shift in Uncertain Computation. Journal of Prospects for Applied Mathematics and Data Analysis, 2 ( 2 ), 22-26 (Doi : https://doi.org/10.54216/PAMDA.020201) |
| Vancouver | Florentin Smarandache, Victor Christianto. A few little steps beyond Knuth’s Boolean Logic Table with Neutrosophic Logic: A Paradigm Shift in Uncertain Computation. Journal of Prospects for Applied Mathematics and Data Analysis, (2023); 2 ( 2 ): 22-26 (Doi : https://doi.org/10.54216/PAMDA.020201) |
| IEEE | Florentin Smarandache, Victor Christianto, A few little steps beyond Knuth’s Boolean Logic Table with Neutrosophic Logic: A Paradigm Shift in Uncertain Computation, Journal of Prospects for Applied Mathematics and Data Analysis, Vol. 2 , No. 2 , (2023) : 22-26 (Doi : https://doi.org/10.54216/PAMDA.020201) |