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• W3200311721 abstract "We introduce residuated ortholattices as a generalization of -- and environment for the investigation of -- orthomodular lattices. We establish a number of basic algebraic facts regarding these structures, characterize orthomodular lattices as those residuated ortholattices whose residual operation is term-definable in the involutive lattice signature, and demonstrate that residuated ortholattices are the equivalent algebraic semantics of an algebraizable propositional logic. We also show that orthomodular lattices may be interpreted in residuated ortholattices via a translation in the spirit of the double-negation translation of Boolean algebras into Heyting algebras, and conclude with some remarks about decidability." @default.
• W3200311721 created "2021-09-27" @default.
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• W3200311721 date "2021-09-18" @default.
• W3200311721 modified "2023-09-25" @default.
• W3200311721 title "Negative Translations of Orthomodular Lattices and Their Logic" @default.
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• W3200311721 doi "https://doi.org/10.4204/eptcs.343.3" @default.
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