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Algebras for Galois-style connections and their discrete duality. (English) Zbl 1195.03059

Discrete duality is a duality between a class of algebras and an associated class of relational systems without a topology. In the paper such a duality is established for classes of bounded distributive lattices with Galois-style pairs of modal operators and for MTL algebras which are the semantic structures for the monoidal t-norm logic MTL.

MSC:

03G25 Other algebras related to logic
03B52 Fuzzy logic; logic of vagueness
06A15 Galois correspondences, closure operators (in relation to ordered sets)
06D50 Lattices and duality
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