Discrete Dualities for Heyting Algebras with Operators
Fundamenta Informaticae - Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk
Logics from Galois connections
International Journal of Approximate Reasoning
Optimal triangular decompositions of matrices with entries from residuated lattices
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Axiomatic systems for rough set-valued homomorphisms of associative rings
International Journal of Approximate Reasoning
Axiomatic characterizations of dual concept lattices
International Journal of Approximate Reasoning
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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.