Geodesic
Orthocomplemented difference lattices with few generators
Kybernetika, Tome 47 (2011) no. 1, pp. 60-73.

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The algebraic theory of quantum logics overlaps in places with certain areas of cybernetics, notably with the field of artificial intelligence (see, e. g., [19, 20]). Recently an effort has been exercised to advance with logics that possess a symmetric difference ([13, 14]) - with so called orthocomplemented difference lattices (ODLs). This paper further contributes to this effort. In [13] the author constructs an ODL that is not set-representable. This example is quite elaborate. A main result of this paper somewhat economizes on this construction: There is an ODL with 3 generators that is not set-representable (and so the free ODL with 3 generators cannot be set-representable). The result is based on a specific technique of embedding orthomodular lattices into ODLs. The ODLs with 2 generators are always set-representable as we show by characterizing the free ODL with 2 generators - this ODL is ${\rm MO}_3 \times 2^4$.
Classification : 03G12, 06C15, 81B10
Keywords: orthomodular lattice; quantum logic; symmetric difference; Gödel's coding; Boolean algebra; free algebra 
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     author = {Matou\v{s}ek, Milan and Pt\'ak, Pavel},
     title = {Orthocomplemented difference lattices with few generators},
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     pages = {60--73},
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     volume = {47},
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     zbl = {1221.06011},
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     url = {http://geodesic.mathdoc.fr/item/KYB_2011__47_1_a4/}
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Matoušek, Milan; Pták, Pavel. Orthocomplemented difference lattices with few generators. Kybernetika, Tome 47 (2011) no. 1, pp. 60-73. http://geodesic.mathdoc.fr/item/KYB_2011__47_1_a4/