Results 151 to 160 of about 781 (187)
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Fuzzy Galois connections categorically
Mathematical Logic Quarterly, 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 Gutierrez Garcia, Dexue Zhang
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Duality for Quasilattices and Galois Connections
Fundamenta Informaticae, 2017The primary goal of the paper is to establish a duality for quasilattices. The main ingredients are duality for semilattices and their representations, the structural analysis of quasilattices as Płonka sums of lattices, and the duality for lattices developed by Hartonas and Dunn.
Anna B. Romanowska, Jonathan D. H. Smith
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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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Logica Universalis, 2007
The connection presented in this paper mirror-links two metamathematical structures, the finitary closure operators, and the compact consistency properties, in such a way that a specification of one structure induces a provably equivalent specification of the other.
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The connection presented in this paper mirror-links two metamathematical structures, the finitary closure operators, and the compact consistency properties, in such a way that a specification of one structure induces a provably equivalent specification of the other.
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A Primer on Galois Connections
Annals of the New York Academy of Sciences, 1993ABSTRACT. The rudiments of the theory of Galois connections (or residuation theory, as it is sometimes called) are provided, together with many examples and applications. Galois connections occur in profusion and are well known to most mathematicians who deal with order theory; they seem to be less known to topologists.
M Erne
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Safety of abstract interpretations for free, via logical relations and Galois connections [PDF]
Science of Computer Programming, 2004 Algebraic properties of logical relations on partially ordered sets are studied. It is shown how to construct a logical relation that extends a collection of base Galois connections to a Galois connection of arbitrary higher-order type.
Roland Backhouse
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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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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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Logical Relations and Galois Connections
2002Algebraic properties of logical relations on partially ordered sets are studied. It is shown how to construct a logical relation that extends a collection of base Galois connections to a Galois connection of arbitrary higher-order type. "Theorems-for-free" is used to show that the construction ensures safe abstract interpretation of parametrically ...
Kevin Backhouse, Roland Carl Backhouse
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