Results 111 to 120 of about 304 (134)

Galois Connections for Flow Algebras

2011
We 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, Michal Terepeta, Hanne Riis Nielson, Flemming Nielson   +3 more
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Triadic fuzzy Galois connections as ordinary connections

Fuzzy Sets and Systems, 2012
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Radim Belohlávek, Petr Osicka
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Logical Relations and Galois Connections

2002
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. "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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Biclosed Binary Relations and Galois Connections

Order, 2001
A biclosed relation between two closure spaces \(E\) and \(E'\) is a binary relation \(R\subseteq E\times E'\) with every row of its matrix representation corresponding to a closed subset of \(E'\) and every column corresponding to a closed subset of \(E\).
Florent Domenach, Bruno Leclerc
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On Galois Connections and Soft Computing

2013
After recalling the different interpretations usually assigned to the term Galois connection, both in the crisp and in the fuzzy case, we survey on several of their applications in Computer Science and specifically, in Soft Computing.
Francisca García-Pardo, Inma P. Cabrera, Pablo Cordero, Manuel Ojeda-Aciego   +3 more
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A Diagram of Galois Connections of Functorial Topologies

Applied Categorical Structures, 2016
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Gabriele Castellini, Stan Dziobiak
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Galois Connections and Pair Algebras

Canadian Journal of Mathematics, 1969
Unless further restricted, P, Q, and R denote arbitrary partially ordered sets whose order relations are all written “≦” .An isotone mapping ϕ: P → Q is said to be residuated if there is an isotone mapping ψ: Q → P such that(RM 1) xϕψ ≧ x for all x i n P;(RM 2) yψϕ ≦ for all y in Q.Let Q* denote the partially ordered set with order relation dual to ...
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A Relational Extension of Galois Connections

2019
In 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, Pablo Cordero, Emilio Muñoz-Velasco, Manuel Ojeda-Aciego   +3 more
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A Primer on Galois Connections

Annals of the New York Academy of Sciences, 1993
ABSTRACT. 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. ERNÉ, J. KOSLOWSKI, A. MELTON, G. E. STRECKER   +3 more
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Galois Connections in Axiomatic Aggregation

2011
We investigate the relations between, on the one hand, Galois connections and the related types of maps and, on the other hand, the axiomatic Arrowian approach for the aggregation (or consensus) problem in lattices. In the latter one wants to "aggregate" n-tuples (n ≥ 2) of elements of a lattice L into an element of this lattice representing their ...
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