کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
397679 | 1438458 | 2014 | 9 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Representing expansions of bounded distributive lattices with Galois connections in terms of rough sets Representing expansions of bounded distributive lattices with Galois connections in terms of rough sets](/preview/png/397679.png)
• We study expansions of bounded distributive lattices equipped with a Galois connection.
• Our results generalize well-known representation theorems by Jónsson and Tarski presented for Boolean algebras with operators.
• The representations are given in terms of rough sets approximation operators and Alexandrov topologies.
• Heyting algebras with a Galois connection can be extended to spatial Heyting algebras with rough set approximation operators.
• Heyting–Brouwer algebras with a Galois connection can be extended to weakly atomic Heyting–Brouwer algebras with rough set approximation operators.
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.
Journal: International Journal of Approximate Reasoning - Volume 55, Issue 1, Part 4, January 2014, Pages 427–435