A1 Refereed original research article in a scientific journal
Representing expansions of bounded distributive lattices with Galois connections in terms of rough sets
Authors: Dzik W, Jarvinen J, Kondo M
Publisher: ELSEVIER SCIENCE INC
Publication year: 2014
Journal: International Journal of Approximate Reasoning
Journal name in source: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
Journal acronym: INT J APPROX REASON
Volume: 55
Issue: 1
First page : 427
Last page: 435
Number of pages: 9
ISSN: 0888-613X
DOI: https://doi.org/10.1016/j.ijar.13.07.005
Abstract
This paper studies expansions of bounded distributive lattices equipped with a Galois connection. We introduce GC-frames and canonical frames for these algebras. The complex algebras of GC-frames are defined in terms of rough set approximation operators. We prove that each bounded distributive lattice with a Galois connection can be embedded into the complex algebra of its canonical frame. We show that for every spatial Heyting algebra L equipped with a Galois connection, there exists a GC-frame such that L is isomorphic to the complex algebra of this frame, and an analogous result holds for weakly atomic Heyting-Brouwer algebras with a Galois connection. In each case of representation, given Galois connections are represented by rough set upper and lower approximations. (C) 2013 Elsevier Inc. All rights reserved.
This paper studies expansions of bounded distributive lattices equipped with a Galois connection. We introduce GC-frames and canonical frames for these algebras. The complex algebras of GC-frames are defined in terms of rough set approximation operators. We prove that each bounded distributive lattice with a Galois connection can be embedded into the complex algebra of its canonical frame. We show that for every spatial Heyting algebra L equipped with a Galois connection, there exists a GC-frame such that L is isomorphic to the complex algebra of this frame, and an analogous result holds for weakly atomic Heyting-Brouwer algebras with a Galois connection. In each case of representation, given Galois connections are represented by rough set upper and lower approximations. (C) 2013 Elsevier Inc. All rights reserved.
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