With the use of a suitable assumption about the structure of the class of experimental filters, it is shown that the sequence of alternating replicas of two filters is their greatest lower bound, as Jauch suggests. A generalization of his suggestion yields the greatest lower bound of a denumerable set of filters. The criteria of admissibility of filters are briefly discussed.

This paper is based on a semantic foundation of quantum logic which makes use of dialog-games. In the first part of the paper the dialogic method is introduced and under the conditions of quantum mechanical measurements the rules of a dialog-game about quantum mechanical propositions are established. In the second part of the paper the quantum mechanical dialog-game is replaced by a calculus of quantum logic. As the main part of the paper we show that the calculus of quantum logic (...) is complete and consistent with respect to the dialogic semantics. Since the dialoggame does not involve the 'excluded middle' the calculus represents a calculus of effective (intuitionistic) quantum logic. In a forthcoming paper it is shown that this calculus is equivalent to a calculus of sequents and more interestingly to a calculus of propositions. With the addition of the 'excluded middle' the latter calculus is a model for the lattice of subspaces of a Hilbert space. (shrink)

It is shown that the uncertainty principle has nothing directly to do with the non-localisability of position and momentum for an individual system on the quantum logical view. The product Δ x· Δ p for localisation of the ranges of position and momentum of an individual system→ ∞ , while the quantities Δ X and Δ P in the uncertainty principle $\Delta X\cdot \Delta P\geq \hslash /2$ , must be given a statistical interpretation on the quantum logical view.