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A category of Galois connections
1987We study Galois connections by examining the properties of three categories. The objects in each category are Galois connections. The categories differ in their hom-sets; in the most general category the morphisms are pairs of functions which commute with the maps of the domain and codomain Galois connections. One of our main results is that one of the
J. M. McDill +2 more
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Hilbert Algebras with Hilbert–Galois Connections
Studia Logica, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sergio A. Celani, Daniela Montangie
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Fuzzy Galois connections categorically
MLQ, 2010The paper deals with closed categories over complete lattice-ordered monoids \((L, \vee, \wedge, \ast, 1)\). Covariant and contravariant fuzzy Galois connections were introduced and examined by \textit{R. Bělohlávek} [Math. Log. Q. 45, No.~4, 497--504 (1999; Zbl 0938.03079)], and \textit{G. Georgescu} and \textit{A. Popescu} [Soft Comput. 7, No.~7, 458-
Javier Gutiérrez García +3 more
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Armstrong systems and Galois connections
2011 IEEE International Conference on Granular Computing, 2011In the paper [1], it is proved that any Galois connection (f, g) on a complete lattice made an Armstrong system F (f, g) . We prove in this short note that the converse holds, that is, for a given Armstrong system R, we can make a Galois connection (φ R , ψ R ) and the original Armstrong system R is identical with the induced Armstrong system F (φR, ψR)
Michiro Kondo, Sho Soneda, Bunpei Yoshii
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Attribute Implication Bases From Galois Connection Structures
Mathematical Methods in the Applied SciencesModeling knowledge systems by determining relationships among key variables have been and currently is a fundamental and nontrivial challenge in real-world scenarios.
Jesus Medina +2 more
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Relational fuzzy Galois connections
2017 Joint 17th World Congress of International Fuzzy Systems Association and 9th International Conference on Soft Computing and Intelligent Systems (IFSA-SCIS), 2017We propose a suitable generalization of the notion of Galois connection whose components are fuzzy relations. We prove that the construction embeds Yao's notion of fuzzy Galois connection as a particular case. Although the natural framework for the proposed notion is that of fuzzy preposets, we also prove that it behaves properly with respect to the ...
Inma P. Cabrera +2 more
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2007
Galois connections can be defined for lattices and for ordered sets. We discuss a rather wide generalisation, which was introduced by Weiqun Xia and has been reinvented under different names: Relational Galois connections between relations. It turns out that the generalised notion is of importance for the original one and can be utilised, e.g., for ...
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Galois connections can be defined for lattices and for ordered sets. We discuss a rather wide generalisation, which was introduced by Weiqun Xia and has been reinvented under different names: Relational Galois connections between relations. It turns out that the generalised notion is of importance for the original one and can be utilised, e.g., for ...
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Galois Connections for Flow Algebras
2011We generalise Galois connections from complete lattices to flow algebras. Flow algebras are algebraic structures that are less restrictive than idempotent semirings in that they replace distributivity with monotonicity and dispense with the annihilation property; therefore they are closer to the approach taken by Monotone Frameworks and other classical
Piotr Filipiuk +3 more
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Triadic fuzzy Galois connections as ordinary connections
Fuzzy Sets and Systems, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Radim Belohlávek, Petr Osicka
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A Relational Extension of Galois Connections
2019In this paper, we focus on a twofold relational generalization of the notion of Galois connection. It is twofold because it is defined between sets endowed with arbitrary transitive relations and, moreover, both components of the connection are relations as well.
Inma P. Cabrera +3 more
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