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Brouwer-Zadeh posets and three-valued Łukasiewicz posets. (English) Zbl 0682.03036
The authors study a Brouwer-Zadeh poset which has the Zadeh completion and the Brouwerian complementation. They give a construction of a three- valued Brouwer-Zadeh poset from a given Brouwer Zadeh poset. The set of all generalized characteristic mappings on a reference space and the set of all generalized orthogonal projections on a Hilbert space are dealt with as intriguing examples of Brouwer-Zadeh posets.
Reviewer: H.Nishimura

##### MSC:
 03G12 Quantum logic 06A05 Total orders 03B52 Fuzzy logic; logic of vagueness 03B45 Modal logic (including the logic of norms) 03B50 Many-valued logic 06C15 Complemented lattices, orthocomplemented lattices and posets
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