Negative Translations of Orthomodular Lattices and Their Logic

@article{Fussner2021NegativeTO,
  title={Negative Translations of Orthomodular Lattices and Their Logic},
  author={Wesley Fussner and Gavin St. John},
  journal={Electronic Proceedings in Theoretical Computer Science},
  year={2021}
}
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… 

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