Geodesic
Ring-like structures with unique symmetric difference related to quantum logic
Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 2, pp. 239-253

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Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.
Keywords: generalized Boolean quasiring, symmetric difference, quantum logic 
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Dorninger, Dietmar; Länger, Helmut; Maczyński, Maciej. Ring-like structures with unique symmetric difference related to quantum logic. Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 2, pp. 239-253. http://geodesic.mathdoc.fr/item/DMGAA_2001_21_2_a8/