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Journal articles on the topic 'Boolean'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Chernoskutov, Yu Yu. "On the Syllogistic of G. Boole." Discourse 7, no. 2 (2021): 5–15. http://dx.doi.org/10.32603/2412-8562-2021-7-2-5-15.

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Introduction. This article focuses on the investigation of Boole’s theory of categorical syllogism, exposed in his book “The Mathematical analysis of Logic”. That part of Boolean legacy has been neglected in the prevailed investigations on the history of logic; the latter provides the novelty of the work presented.Methodology and sources. The formal reconstruction of the methods of algebraic presentation of categorical syllogism, as it is exposed in the original work of Boole, is conducted. The character of Boolean methods is investigated in the interconnections with the principles of symbolic

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2

Allart, Emilie, Joachim Niehren, and Cristian Versari. "Exact Boolean Abstraction of Linear Equation Systems." Computation 9, no. 11 (2021): 113. http://dx.doi.org/10.3390/computation9110113.

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We study the problem of how to compute the boolean abstraction of the solution set of a linear equation system over the positive reals. We call a linear equation system ϕ exact for the boolean abstraction if the abstract interpretation of ϕ over the structure of booleans is equal to the boolean abstraction of the solution set of ϕ over the positive reals. Abstract interpretation over the booleans is thus complete for the boolean abstraction when restricted to exact linear equation systems, while it is not complete more generally. We present a new rewriting algorithm that makes linear equation

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3

Huang, Jing Lian, Su Duo Li, Yong Liu, and Ke Yan Deng. "On Analysis and Judgment of Balance for Boolean Functions by E-Derivative." Applied Mechanics and Materials 643 (September 2014): 130–35. http://dx.doi.org/10.4028/www.scientific.net/amm.643.130.

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Using the derivative of the Boolean function and the e-derivative defined by ourselves as research tools and deeply into the internal structure of Boolean, we study the issues of the analysis and judgment of balance for Boolean functions. We get that the linear functions and the nonzero derivative of the product of two linear functions are balanced functions, and the product of two linear functions are not balanced functions. We also obtain the quadratic homogeneous Booleans are not all balanced function. Besides, we deduce the theorem which determine the sum of linear function and balanced fu

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4

De Villiers, Michael D. "Teaching Modeling and Axiomatization with Boolean Algebra." Mathematics Teacher 80, no. 7 (1987): 528–32. http://dx.doi.org/10.5951/mt.80.7.0528.

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Traditionally, Boolean algebra is largely taught in connection with computer programming courses, logic, or set theory. Since Boolean algebra arose from George Boole's application of algebraic principles to the study of logic in 1854, this approach would seem natural.

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5

Chajda, I., and M. Kotrle. "Boolean semirings." Czechoslovak Mathematical Journal 44, no. 4 (1994): 763–67. http://dx.doi.org/10.21136/cmj.1994.128495.

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6

Madsen, Magnus, Jaco van de Pol, and Troels Henriksen. "Fast and Efficient Boolean Unification for Hindley-Milner-Style Type and Effect Systems." Proceedings of the ACM on Programming Languages 7, OOPSLA2 (2023): 516–43. http://dx.doi.org/10.1145/3622816.

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As type and effect systems become more expressive there is an increasing need for efficient type inference. We consider a polymorphic effect system based on Boolean formulas where inference requires Boolean unification. Since Boolean unification involves semantic equivalence, conventional syntax-driven unification is insufficient. At the same time, existing Boolean unification techniques are ill-suited for type inference. We propose a hybrid algorithm for solving Boolean unification queries based on Boole’s Successive Variable Elimination (SVE) algorithm. The proposed approach builds on severa

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7

Ali M. Ali Rushdi, Ali M. Ali Rushdi. "Satisfiability in Big Boolean Algebras via Boolean-Equation Solving." journal of King Abdulaziz University Engineering Sciences 28, no. 1 (2017): 3–18. http://dx.doi.org/10.4197/eng.28-1.1.

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This paper studies Satisfiability (SAT) in finite atomic Boolean algebras larger than the two-valued one B2, which are named big Boolean algebras. Unlike the formula ݃(ࢄ (in the SAT problem over B2, which is either satisfiable or unsatisfiable, this formula for the SAT problem over a big Boolean algebra could be unconditionally satisfiable, conditionally satisfiable, or unsatisfiable depending on the nature of the consistency condition of the Boolean equation {݃(ࢄ = (1}, since this condition could be an identity, a genuine equation, or a contradiction. The paper handles this latter SAT problem

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8

Wehrung, Friedrich. "Boolean universes above Boolean models." Journal of Symbolic Logic 58, no. 4 (1993): 1219–50. http://dx.doi.org/10.2307/2275140.

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AbstractWe establish several first- or second-order properties of models of first-order theories by considering their elements as atoms of a new universe of set theory and by extending naturally any structure of Boolean model on the atoms to the whole universe. For example, complete f-rings are “boundedly algebraically compact” in the language (+, −, ·, ∧, ∨, ≤), and the positive cone of a complete l-group with infinity adjoined is algebraically compact in the language (+, ∨, ≤). We also give an example with any first-order language. The proofs can be translated into “naive set theory” in a un

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9

Studenic, Paul, David Felson, Maarten de Wit, et al. "Testing different thresholds for patient global assessment in defining remission for rheumatoid arthritis: are the current ACR/EULAR Boolean criteria optimal?" Annals of the Rheumatic Diseases 79, no. 4 (2020): 445–52. http://dx.doi.org/10.1136/annrheumdis-2019-216529.

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ObjectivesThis study aimed to evaluate different patient global assessment (PGA) cut-offs required in the American College of Rheumatology/European League Against Rheumatism (ACR/EULAR) Boolean remission definition for their utility in rheumatoid arthritis (RA).MethodsWe used data from six randomised controlled trials in early and established RA. We increased the threshold for the 0–10 score for PGA gradually from 1 to 3 in steps of 0.5 (Boolean1.5 to Boolean3.0) and omitted PGA completely (BooleanX) at 6 and 12 months. Agreement with the index-based (Simplified Disease Activity Index (SDAI))

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10

Kadioglu, Serdar, Elton Yechao Zhu, Gili Rosenberg, et al. "BoolXAI: Explainable AI Using Expressive Boolean Formulas." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 28 (2025): 28900–28906. https://doi.org/10.1609/aaai.v39i28.35157.

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In this tool paper, we design, develop, and release BoolXAI, an interpretable machine learning classification approach for Explainable AI (XAI) based on expressive Boolean formulas. The Boolean formula defines a logical rule with tunable complexity according to which input data are classified. Beyond the classical conjunction and disjunction, BoolXAI offers expressive operators such as AtLeast, AtMost, and Choose and their parameterization. This provides higher expressiveness compared to rigid rules- and tree-based approaches. We show how to train BoolXAI classifiers effectively using native l

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11

Rudeanu, Sergiu. "On the Decomposition of Boolean Functions via Boolean Equations." JUCS - Journal of Universal Computer Science 10, no. (9) (2004): 1294–301. https://doi.org/10.3217/jucs-010-09-1294.

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We propose an alternative solution to the problems solved in [1]. Our aim is to advocate the efficiency of algebraic methods for the solution of the Boolean equations which occur in the decomposition of Boolean functions.

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12

Stempel, Rachel. "BOOLEAN." Minnesota review 2022, no. 98 (2022): 17. http://dx.doi.org/10.1215/00265667-9563639.

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13

Ricci, Gabriele. "Boolean matrices ... neither Boolean nor matrices." Discussiones Mathematicae - General Algebra and Applications 20, no. 1 (2000): 141. http://dx.doi.org/10.7151/dmgaa.1012.

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14

Reith, Steffen, and Klaus W. Wagner. "On boolean lowness and boolean highness." Theoretical Computer Science 261, no. 2 (2001): 305–21. http://dx.doi.org/10.1016/s0304-3975(00)00146-8.

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15

Khuzam, Hazar Abu, and Adil Yaqub. "Generalized Boolean and Boolean-like rings." International Journal of Algebra 7 (2013): 429–38. http://dx.doi.org/10.12988/ija.2013.2894.

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16

Sachwanowicz, Wojcech. "Boolean powers over incomplete boolean algebras." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 36, no. 5 (1990): 431–40. http://dx.doi.org/10.1002/malq.19900360508.

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17

Cherchi, Gianmarco, Fabio Pellacini, Marco Attene, and Marco Livesu. "Interactive and Robust Mesh Booleans." ACM Transactions on Graphics 41, no. 6 (2022): 1–14. http://dx.doi.org/10.1145/3550454.3555460.

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Boolean operations are among the most used paradigms to create and edit digital shapes. Despite being conceptually simple, the computation of mesh Booleans is notoriously challenging. Main issues come from numerical approximations that make the detection and processing of intersection points inconsistent and unreliable, exposing implementations based on floating point arithmetic to many kinds of degeneracy and failure. Numerical methods based on rational numbers or exact geometric predicates have the needed robustness guarantees, that are achieved at the cost of increased computation times tha

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18

Espitia, Helbert, José Soriano, Iván Machón, and Hilario López. "Compact Fuzzy Systems Based on Boolean Relations." Applied Sciences 11, no. 4 (2021): 1793. http://dx.doi.org/10.3390/app11041793.

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This document presents some considerations and procedures to design a compact fuzzy system based on Boolean relations. In the design process, a Boolean codification of two elements is extended to a Kleene’s of three elements to perform simplifications for obtaining a compact fuzzy system. The design methodology employed a set of considerations producing equivalent expressions when using Boole and Kleene algebras establishing cases where simplification can be carried out, thus obtaining compact forms. In addition, the development of two compact fuzzy systems based on Boolean relations is shown,

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19

Rushdi, Ali Muhammad Ali, and Waleed Ahmad. "Digital Circuit Design Utilizing Equation Solving over ‘Big’ Boolean Algebras." International Journal of Mathematical, Engineering and Management Sciences 3, no. 4 (2018): 404–28. http://dx.doi.org/10.33889/ijmems.2018.3.4-029.

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A task frequently encountered in digital circuit design is the solution of a two-valued Boolean equation of the form h(X,Y,Z)=1, where h: B_2^(k+m+n)→ B_2 and X,Y, and Z are binary vectors of lengths k, m, and n, representing inputs, intermediary values, and outputs, respectively. The resultant of the suppression of the variables Y from this equation could be written in the form g(X,Z)=1 where g: B_2^(k+n)→ B_2. Typically, one needs to solve for Z in terms of X, and hence it is unavoidable to resort to ‘big’ Boolean algebras which are finite (atomic) Boolean algebras larger than the two-valued

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20

Takeuti, Gaisi. "Boolean Simple Groups and Boolean Simple Rings." Journal of Symbolic Logic 53, no. 1 (1988): 160. http://dx.doi.org/10.2307/2274435.

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21

Avilés, Antonio. "Boolean Metric Spaces and Boolean Algebraic Varieties." Communications in Algebra 32, no. 5 (2004): 1805–22. http://dx.doi.org/10.1081/agb-120029903.

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22

MOVSISYAN, YU M., and V. A. ASLANYAN. "SUPER-BOOLEAN FUNCTIONS AND FREE BOOLEAN QUASILATTICES." Discrete Mathematics, Algorithms and Applications 06, no. 02 (2014): 1450024. http://dx.doi.org/10.1142/s1793830914500244.

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A Boolean quasilattice is an algebra with hyperidentities of the variety of Boolean algebras. In this paper, we give a functional representation of the free n-generated Boolean quasilattice with two binary, one unary and two nullary operations. Namely, we define the concept of super-Boolean function and prove that the free Boolean quasilattice with two binary, one unary and two nullary operations on n free generators is isomorphic to the Boolean quasilattice of super-Boolean functions of n variables.

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23

Kusraev, A. G., and S. S. Kutateladze. "Prolegomena to Boolean Valued Analysis: Boolean Toposes." Siberian Mathematical Journal 66, no. 1 (2025): 129–67. https://doi.org/10.1134/s0037446625010124.

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24

Gudder, Stan, and Frédéric Latrémolière. "Boolean inner-product spaces and Boolean matrices." Linear Algebra and its Applications 431, no. 1-2 (2009): 274–96. http://dx.doi.org/10.1016/j.laa.2009.02.028.

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25

Takeuti, Gaisi. "Boolean simple groups and boolean simple rings." Journal of Symbolic Logic 53, no. 1 (1988): 160–73. http://dx.doi.org/10.1017/s0022481200029005.

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Let be a complete Boolean algebra and G a finite simple group in the Scott-Solovay -valued model V() of set theory. If we observe G outside V(), then we get a new group which is denoted by Ĝ. In general, Ĝ is not finite nor simple. Nevertheless Ĝ satisfies every property satisfied by a finite simple group with some translation. In this way, we can get a class of groups for which we can use a well-developed theory of the finite simple groups. We call Ĝ Boolean simple if G is simple in some V(). In the same way we define Boolean simple rings. The main purpose of this paper is a study of structur

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26

TAKAHASHI, Makoto. "Completeness of Boolean powers of Boolean algebras." Journal of the Mathematical Society of Japan 40, no. 3 (1988): 445–56. http://dx.doi.org/10.2969/jmsj/04030445.

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27

Couceiro, Miguel, Jean-Luc Marichal, and Tamás Waldhauser. "Locally monotone Boolean and pseudo-Boolean functions." Discrete Applied Mathematics 160, no. 12 (2012): 1651–60. http://dx.doi.org/10.1016/j.dam.2012.03.006.

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28

Buszkowski, Wojciech. "Embedding Boolean Structures into Atomic Boolean Structures." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 32, no. 13-16 (1986): 227–28. http://dx.doi.org/10.1002/malq.19860321307.

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29

Pushpalatha, K., and V. M.L.Hima Bindu. "A Note on Boolean Like Algebras." International Journal of Engineering & Technology 7, no. 4.10 (2018): 1015. http://dx.doi.org/10.14419/ijet.v7i4.10.26660.

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In this paper we develop on abstract system: viz Boolean-like algebra and prove that every Boolean algebra is a Boolean-like algebra. A necessary and sufficient condition for a Boolean-like algebra to be a Boolean algebra has been obtained. As in the case of Boolean ring and Boolean algebra, it is established that under suitable binary operations the Boolean-like ring and Boolean-like algebra are equivalent abstract structures.

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30

Pushpalatha, K., and . "Some Contributions to Boolean like near Rings." International Journal of Engineering & Technology 7, no. 3.34 (2018): 670. http://dx.doi.org/10.14419/ijet.v7i3.34.19413.

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In this paper we extend Foster’s Boolean-like ring to Near-rings. We introduce the concept of a Boolean like near-ring. A near-ring N is said to be a Boolean-like near-ring if the following conditions hold: (i) a+a = 0 for all aÎ N , (ii) ab(a+b+ab) = ba for all a, b Î N and (iii) abc = acb for all a,b, c Î N (right weak commutative law). We have proved that every Boolean ring is a Boolean like near-ring. An example is given to show that the converse is not true. We prove that if N is a Boolean near-ring then conditions (i) and (ii) of the above definition are equivalent. We also proved that a

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31

Frické, Martin. "Boolean Logic." KNOWLEDGE ORGANIZATION 48, no. 2 (2021): 177–91. http://dx.doi.org/10.5771/0943-7444-2021-2-177.

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The article describes and explains Boolean logic (or Boolean algebra) in its two principal forms: that of truth-values and the Boolean connectives and, or, and not, and that of set membership and the set operations of intersection, union and complement. The main application areas of Boolean logic to knowledge organization, namely post-coordinate indexing and search, are introduced and discussed. Some wider application areas are briefly mentioned, such as: propositional logic, the Shannon-style approach to electrical switching and logic gates, computer programming languages, probability theory

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32

Vardi, Moshe Y. "Boolean satisfiability." Communications of the ACM 57, no. 3 (2014): 5. http://dx.doi.org/10.1145/2578043.

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33

Reddy, J. K. "Boolean Algebra." IETE Journal of Education 28, no. 4 (1987): 153–58. http://dx.doi.org/10.1080/09747338.1987.11436173.

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34

Brinn, L. W. "Boolean algebra." International Journal of Mathematical Education in Science and Technology 20, no. 6 (1989): 799–807. http://dx.doi.org/10.1080/0020739890200602.

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35

Hodgkin, J. "Boolean yeast?" Trends in Genetics 14, no. 2 (1998): 53. http://dx.doi.org/10.1016/s0168-9525(98)01411-5.

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36

McAllester, David, and Ramin Zabih. "Boolean classes." ACM SIGPLAN Notices 21, no. 11 (1986): 417–23. http://dx.doi.org/10.1145/960112.28740.

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37

Vechtomov, E. M. "Boolean rings." Mathematical Notes of the Academy of Sciences of the USSR 39, no. 2 (1986): 101–3. http://dx.doi.org/10.1007/bf01159890.

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38

Wang, Chi. "Boolean minors." Discrete Mathematics 141, no. 1-3 (1995): 237–58. http://dx.doi.org/10.1016/0012-365x(93)e0191-6.

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39

Boros, E., P. L. Hammer, and J. N. Hooker. "Boolean regression." Annals of Operations Research 58, no. 3 (1995): 201–26. http://dx.doi.org/10.1007/bf02032132.

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40

Okhotin, Alexander. "Boolean grammars." Information and Computation 194, no. 1 (2004): 19–48. http://dx.doi.org/10.1016/j.ic.2004.03.006.

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41

Bishop, Barbara A. "Beware Boolean:." College & Undergraduate Libraries 1, no. 2 (1994): 23–24. http://dx.doi.org/10.1300/j106v01n02_03.

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42

Min, Yinghua, Zhongcheng Li, and Zhuxing Zhao. "Boolean process." Science in China Series E: Technological Sciences 40, no. 3 (1997): 250–57. http://dx.doi.org/10.1007/bf02916600.

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43

Banković, Dragić. "Boolean inequations." Discrete Mathematics 307, no. 6 (2007): 750–55. http://dx.doi.org/10.1016/j.disc.2006.07.006.

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44

Crama, Yves, and Peter L. Hammer. "Boolean Functions." Discrete Applied Mathematics 161, no. 1-2 (2013): 315. http://dx.doi.org/10.1016/j.dam.2012.07.021.

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45

Bubeck, Uwe, and Hans Kleine Büning. "Encoding Nested Boolean Functions as Quantified Boolean Formulas." Journal on Satisfiability, Boolean Modeling and Computation 8, no. 1-2 (2012): 101–16. http://dx.doi.org/10.3233/sat190092.

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46

Beasley, Leroy B., Kyung-Tae Kang, and Seok-Zun Song. "CHARACTERIZATIONS OF BOOLEAN RANK PRESERVERS OVER BOOLEAN MATRICES." Pure and Applied Mathematics 21, no. 2 (2014): 121–28. http://dx.doi.org/10.7468/jksmeb.2014.21.2.121.

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47

Vechtomov, E. M. "Annihilator characterizations of Boolean rings and Boolean lattices." Mathematical Notes 53, no. 2 (1993): 124–29. http://dx.doi.org/10.1007/bf01208314.

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48

Kleine Büning, Hans, K. Subramani, and Xishun Zhao. "Boolean Functions as Models for Quantified Boolean Formulas." Journal of Automated Reasoning 39, no. 1 (2007): 49–75. http://dx.doi.org/10.1007/s10817-007-9067-0.

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49

Leech, Jonathan, and Matthew Spinks. "Skew Boolean algebras derived from generalized Boolean algebras." Algebra universalis 58, no. 3 (2008): 287–302. http://dx.doi.org/10.1007/s00012-008-2069-x.

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50

Steinbach, Bernd, and Christian Posthoff. "Boolean differential equations: A common model for classes, lattices, and arbitrary sets of Boolean functions." Facta universitatis - series: Electronics and Energetics 28, no. 1 (2015): 51–76. http://dx.doi.org/10.2298/fuee1501051s.

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The Boolean Differential Calculus (BDC) significantly extends the Boolean Algebra because not only Boolean values 0 and 1, but also changes of Boolean values or Boolean functions can be described. A Boolean Differential Equation (BDe) is a Boolean equation that includes derivative operations of the Boolean Differential Calculus. This paper aims at the classification of BDEs, the characterization of the respective solutions, algorithms to calculate the solution of a BDe, and selected applications. We will show that not only classes and arbitrary sets of Boolean functions but also lattices of Bo

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