Abstract
Two axiomatic approaches to quantum mechanics are compared : the quantum-logic approach and the transition-probabi1ity spaces approach. It is shown that the quantum-logic approach is more general than the transition-probability spaces approach. Necessary and sufficient conditions -for the equivalence of these approaches are found. As a generalization of the above approaches, a notion of an orthogonality space is introduced. Conditions under which an orthogonality space can be represented in a generalized Hilbert space are investigated.
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