Representing expansions of bounded distributive lattices with Galois connections in terms of rough sets
We study expansions of bounded distributive lattices equipped with a Galois connection. Our results generalize well-known representation theorems by Jnsson 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. HeytingBrouwer algebras with a Galois connection can be extended to weakly atomic HeytingBrouwer algebras with rough set approximation operators.
rough sets representation theorems heyting algebras heytingbrouwer algebras intuitionistic logic