Effectible residuated lattices and \(n\)-th roots (Q983038)
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scientific article; zbMATH DE number 5762244
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Effectible residuated lattices and \(n\)-th roots |
scientific article; zbMATH DE number 5762244 |
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Effectible residuated lattices and \(n\)-th roots (English)
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28 July 2010
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The author introduces ``effectible residuated lattices'' and ``effectible Girard algebras'' as generalizations of various structures considered by Höhle and others, which, in turn, are generalizations of many structures arising as the algebras of many-valued logics as well as the order-theoretic counterparts of classes of bounded linear operators in Hilbert space. The present paper gives sufficient conditions for a Girard algebra to be an effect algebra. Similar conditions are given for residuated lattices to coincide with a suitable generalization of effect algebras.
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residuated lattice
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Girard algebra
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MV-algebra
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Höhle monoid
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effect algebra
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