Orthomodular lattices can be converted into left residuated l-groupoids

Abstract

We show that every orthomodular lattice can be considered as a left residuated l-groupoid satisfying divisibility, antitony, the double negation law and three more additional conditions expressed in the language of residuated structures. Also conversely, every left residuated l-groupoid satisfying the mentioned conditions can be organized into an orthomodular lattice.

Cited by in corpus (4)

• Negative Translations of Orthomodular Lattices and Their Logic
• Unsharp residuation in effect algebras
• Residuation in modular lattices and posets
• Implication in weakly and dually weakly orthomodular lattices