On the Logical Foundations of the Jauch-Piron Approach to Quantum Physics

Gianpiero Cattaneo, Carlo Dalla Pozza, Claudio Garola +1 more

WilhelmK. Essler, Gerhard Zoubek

Alexandru Baltag, Sonja Smets

In this paper we show how ideas coming from two areas of research in logic can reinforce each other. The first such line of inquiry concerns the “dynamic turn” in logic and especially the formalisms inspired by Propositional Dynamic Logic (PDL); while the second line concerns research into the logical foundations of Quantum Physics, and in particular the area known as Operational Quantum Logic, as developed by Jauch and Piron (Helve Phys Acta 42:842–848, 1969 ), Piron (Foundations of Quantum Physics, 1976 ). By bringing these areas together we explain the basic ingredients of Dynamic Quantum Logic, a new direction of research in the logical foundations of physics.

Hans Reinchenbach

Michal Hroch, Pavel Pták

We show in this note that if [Formula: see text] is a Boolean subalgebra of the lattice quantum logic [Formula: see text], then each state on [Formula: see text] can be extended over [Formula: see text] as a Jauch–Piron state provided [Formula: see text] is Jauch–Piron unital with respect to [Formula: see text] (i.e. for each nonzero [Formula: see text], there is a Jauch–Piron state [Formula: see text] on [Formula: see text] such that [Formula: see text]). We then discuss this result for the case of [Formula: see text] being the Hilbert space logic [Formula: see text] and [Formula: see text] being a set-representable logic.

Gottfried T. R�ttimann