Boolean embeddings of orthomodular sets and quantum logic
Neal Zierler, Michael Schlessinger · Duke Mathematical Journal · 1965
By a “quantum logic” we mean a pair F, P where P is a set and F is a set of functions from P to the closed real unit interval satisfying three postulates which we describe in intuitive terms here. Cf. [2], [4], [7]. P may be interpreted as the set of events and F the set of states of a “physical system”, and f(x) then becomes the probability of occurrence of the event x in the state f. Since the outcome of an experiment is an estimate for some f(x), or a collection of such estimates, it is natural to identify events which cannot be distinguished by experiment.