On representations of logics. (English) Zbl 0531.03040

This paper continues an earlier paper by the author [Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 32, 351-360 (1980; Zbl 0453.03066)] in which an embedding of a logic L (i.e. a special orthomodular orthoposet) into the lattice of all f-closed subspaces \(L_ f(V)\) of a vector space V with the Hermitian form f was found. In the present paper the author proves that \(L_ f(V)\) has the Hilbert property \((M+M^{\perp}=V\) for all \(M\in L_ f(V)\) iff the supremum \(a\vee e\) exists in L for any \(a\in L\) and any atom \(e\in L\).
Reviewer: L.Esakia


03G12 Quantum logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03B60 Other nonclassical logic


Zbl 0453.03066
Full Text: EuDML


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