The dynamic turn in quantum logic

Alexandru Baltag

Sonja Smets

pp. 753-773

in: Sonja Smets, Johan van Benthem (eds), Logic meets physics, Synthese 186 (3), 2012.

Abstract

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.