Geodesic
The axioms for implication in orthologic
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 1, pp. 15-21.

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We set up axioms characterizing logical connective implication in a logic derived by an ortholattice. It is a natural generalization of an orthoimplication algebra given by J. C. Abbott for a logic derived by an orthomodular lattice.
Classification : 03G12, 03G25, 06C15
Keywords: ortholattice; orthoimplication; orthologic 
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Chajda, Ivan. The axioms for implication in orthologic. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 1, pp. 15-21. http://geodesic.mathdoc.fr/item/CMJ_2008__58_1_a1/