Orthomodular posets can be organized as conditionally residuated structures. (English) Zbl 1320.06003

A conditionally residuated structure is a poset bounded by \(0,1\), endowed with a partial binary operation \(\to\) and a partial multiplication where \(x\cdot y\) is defined if and only if \(x\to 0\leq y\), with unit \(1\), and satisfying commutativity in the strong sense, such that the residuation axioms are satisfied in the weak sense. The main result characterizes those structures which have orthomodular poset reduct.


06A11 Algebraic aspects of posets
06C15 Complemented lattices, orthocomplemented lattices and posets
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