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arXiv · 1312.6263

Representing distributive lattices with Galois connections in terms of rough sets

Wojciech Dzik·Jouni Järvinen·Michiro Kondo
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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.

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Wojciech Dzik, Jouni Järvinen, Michiro Kondo. 2013-12-21. Representing distributive lattices with Galois connections in terms of rough sets. https://doi.org/10.1016/j.ijar.2013.07.005

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