PROPERTIES OF BOOLEAN ORTHOPOSETS

A Boolean orthoposet is the orthoposet P fulfilling the following cond ition: If a, b is-an-element-of P and a AND h = 0, then a perpendicula r-to b. This condition seems to be a sound generalization of distribut ivity in orthoposets. Also, the class of (orthomodular) Boolean orthop osets may play an interesting role in quantum logic theory. This class is wide enough and, on the other hand, enjoys some properties of Bool ean algebras. In this paper we summarize results on Boolean orthoposet s involving distributivity, set representation, properties of the stat e space, existence of Jauch-Piron states, and results concerning ortho completeness and completion.