On a possible empirical meaning of meets and joins for quantum propositions (Q762150)

According to the Jauch-Piron approach to quantum logic, the logical operations of meet and join are associated with ''infinite sequences of alternate pairs'' of measurements of constituent propositions. This is their ''empirical meaning'', which is generally admitted to be somewhat imprecise. The present author however, intends to develop this in a well- defined way. He seeks to give a precise meaning to the ''infinite sequences'' by applying the theory of limits to probability expressions for repeated experiments. Furthermore he extends his argument to non- countably infinite sequences, with a final suggestion that meets and joins might be understood as Dedekind's cuts, in analogy with the irrationals. The argument is interesting, and probably important to the Jauch-Piron school. However it is arguable to what extent an ''empirical meaning'' could be involved.