Quantum logic and physics

Peter Mittelstaedt

M. L. Dalla Chiara

Martin Strauss

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.

M. Strauss

J.A.J. van Leunen

This is part of a slide presentation. It treats logic systems that relate to the foundation of physics. Classical logic is well known. Traditional quantum logic has a weaker structure and is often assigned as the base of quantum physics. Hilbert logic restricts quantum logic, such that it fits better with Hilbert spaces.