Galois connection based abstract interpretations for strictness analysis

2006 ◽  
pp. 98-127 ◽  
Author(s):  
Patrick Cousot ◽  
Radhia Cousot
Keyword(s):  
Galois Connection ◽  
Strictness Analysis

scholarly journals ON THE PARTITION MONOID AND SOME RELATED SEMIGROUPS

2010 ◽  
Vol 83 (2) ◽  
pp. 273-288 ◽  
Author(s):  
D. G. FITZGERALD ◽  
KWOK WAI LAU
Keyword(s):  
Transformation Semigroup ◽  
Galois Connection ◽  
Inverse Semigroups ◽  
Natural Order ◽  
Binary Relations ◽  
Ideal Lattices ◽  
New Interpretation ◽  
Semigroup Of Transformations ◽  
The Ideal

AbstractThe partition monoid is a salient natural example of a *-regular semigroup. We find a Galois connection between elements of the partition monoid and binary relations, and use it to show that the partition monoid contains copies of the semigroup of transformations and the symmetric and dual-symmetric inverse semigroups on the underlying set. We characterize the divisibility preorders and the natural order on the (straight) partition monoid, using certain graphical structures associated with each element. This gives a simpler characterization of Green’s relations. We also derive a new interpretation of the natural order on the transformation semigroup. The results are also used to describe the ideal lattices of the straight and twisted partition monoids and the Brauer monoid.

scholarly journals A constructive Galois connection between closure and interior

2012 ◽  
Vol 77 (4) ◽  
pp. 1308-1324 ◽  
Author(s):  
Francesco Ciraulo ◽  
Giovanni Sambin
Keyword(s):  
Galois Connection ◽  
Classical Correspondence ◽  
Intuitionistic Version

AbstractWe construct a Galois connection between closure and interior operators on a given set. All arguments are intuitionistically valid. Our construction is an intuitionistic version of the classical correspondence between closure and interior operators via complement.

scholarly journals Noise–Disturbance Relation and the Galois Connection of Quantum Measurements

2019 ◽  
Vol 49 (6) ◽  
pp. 492-505 ◽  
Author(s):  
Claudio Carmeli ◽  
Teiko Heinosaari ◽  
Takayuki Miyadera ◽  
Alessandro Toigo
Keyword(s):  
Quantum Measurements ◽  
Galois Connection ◽  
Noise Disturbance

M-Fuzzifying Approximation Spaces, M-Fuzzifying Pretopological Spaces and M-Fuzzifying Closure Spaces

2020 ◽  
Vol 16 (03) ◽  
pp. 609-626
Author(s):  
Anand P. Singh ◽  
I. Perfilieva
Keyword(s):  
Significant Role ◽  
Category Theory ◽  
Galois Connection ◽  
Fuzzy Relations ◽  
Approximation Spaces ◽  
Closure Spaces

In category theory, Galois connection plays a significant role in developing the connections among different structures. The objective of this work is to investigate the essential connections among several categories with a weaker structure than that of [Formula: see text]-fuzzifying topology, viz. category of [Formula: see text]-fuzzifying approximation spaces based on reflexive [Formula: see text]-fuzzy relations, category of [Formula: see text]-fuzzifying pretopological spaces and the category of [Formula: see text]-fuzzifying interior (closure) spaces. The interrelations among these structures are shown via the functorial diagram.

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