Abstract
A D-algebra is a generalization of a D-poset in which a partial order is not assumed. However, if a D-algebra is equipped with a natural partial order, then it becomes a D-poset. It is shown that D-algebras and effect algebras are equivalent algebraic structures. This places the partial operation ⊝ for a D-algebra on an equal footing with the partial operation ⊕ for an effect algebra. An axiomatic structure called an effect stale-space is introduced. Such spaces provide an operational interpretation for the partial operations ⊕ and ⊝. Finally, a relationship between effect-state spaces and torsion free interval effect algebras is demonstrated.
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Gudder, S. D-algebras. Found Phys 26, 813–822 (1996). https://doi.org/10.1007/BF02058635
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DOI: https://doi.org/10.1007/BF02058635