Geodesic
Symmetric difference on orthomodular lattices and $Z_2$-valued states
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 4, pp. 535-547.

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The investigation of orthocomplemented lattices with a symmetric difference initiated the following question: Which orthomodular lattice can be embedded in an orthomodular lattice that allows for a symmetric difference? In this paper we present a necessary condition for such an embedding to exist. The condition is expressed in terms of $Z_2$-valued states and enables one, as a consequence, to clarify the situation in the important case of the lattice of projections in a Hilbert space.
Classification : 03G12, 06A15, 28E99, 81P10
Keywords: orthomodular lattice; quantum logic; symmetric difference; Boolean algebra; group-valued state 
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Matoušek, Milan; Pták, Pavel. Symmetric difference on orthomodular lattices and $Z_2$-valued states. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 4, pp. 535-547. http://geodesic.mathdoc.fr/item/CMUC_2009__50_4_a3/