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Lattice properties of ring-like quantum logics. (English) Zbl 0967.03055

Int. J. Theor. Phys. 39, No. 4, 1015-1026 (2000).

Generalized Boolean quasirings are models of quantum logics. They might be defined by means of partial generalized Boolean quasirings which are in a one-to-one correspondence with bounded lattices with an involutory antiautomorphism. Connections between properties of these two structures are studied. Under certain assumptions, the associativity of the \(+\)-operation implies that a Boolean ring is obtained, i.e. the quantum system is classical.

Reviewer: Josef Tkadlec (Praha)

Cited in 9 Documents

MSC:

03G12	Quantum logic
81P10	Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)

Keywords:

generalized Boolean quasiring; quantum logic

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