Representing expansions of bounded distributive lattices with Galois connections in terms of rough sets

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• 作者：Wojciech Dzik ; Jouni J盲rvinen ; Michiro Kondo
• 关键词：Rough sets ; Heyting algebras ; Heyting&ndash ; Brouwer algebras ; Intuitionistic logic ; Representation theorems
• 刊名：International Journal of Approximate Reasoning
• 出版年：January, 2014
• 年：2014
• 卷：55
• 期：1
• 页码：427-435
• 全文大小：251 K

文摘

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.