On cardinalities of row spaces of Boolean matrices.
J. Konieczny (1992)
Semigroup forum
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J. Konieczny (1992)
Semigroup forum
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W. Li, M.C. Zhang (1995)
Semigroup forum
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Koriolan Gilezan (1980)
Publications de l'Institut Mathématique
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Gabriele Ricci (2000)
Discussiones Mathematicae - General Algebra and Applications
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Boolean matrices, the incidence matrices of a graph, are known not to be the (universal) matrices of a Boolean algebra. Here, we also show that their usual composition cannot make them the matrices of any algebra. Yet, later on, we "show" that it can. This seeming paradox comes from the hidden intrusion of a widespread set-theoretical (mis) definition and notation and denies its harmlessness. A minor modification of this standard definition might fix it.
Banković, Dragić (1998)
Novi Sad Journal of Mathematics
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Dragić Banković (1989)
Publications de l'Institut Mathématique
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S. Rudeanu (1970)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Steven Garavaglia, J. M. Plotkin (1984)
Colloquium Mathematicae
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Mihai Popa (2009)
Colloquium Mathematicae
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The paper presents several combinatorial properties of the boolean cumulants. A consequence is a new proof of the multiplicative property of the boolean cumulant series that can be easily adapted to the case of boolean independence with amalgamation over an algebra.
Wroński, Stanisław (2015-10-26T10:14:52Z)
Acta Universitatis Lodziensis. Folia Mathematica
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D. Banković (1987)
Matematički Vesnik
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Sergiu Rudeanu (1998)
Mathware and Soft Computing
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An abstract form of modus ponens in a Boolean algebra was suggested in [1]. In this paper we use the general theory of Boolean equations (see e.g. [2]) to obtain a further generalization. For a similar research on Boolean deduction theorems see [3].