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On quantic conuclei in orthomodular lattices. (English) Zbl 0865.03051

Summary: We study the lattice of quantic conuclei for orthomodular lattices. We show that under certain conditions we can get a complete characterization of all quantic conuclei. The thing to note is that we use a noncommutative, nonassociative disjunction operation which can be thought of as from noncommutative, nonassociative linear logic.

MSC:

03G12 Quantum logic
06C15 Complemented lattices, orthocomplemented lattices and posets
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03G30 Categorical logic, topoi
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