A phenomenological foundation of quantum logic

Andrei Galiautdinov

Claudio Garola

Peter Mittelstaedt, Ernst-Walther Stachow

David Geoffrey Holdsworth

The contents of this paper consist of two independent but correlated topics. In Part I the history of nineteenth and twentieth century philosophy of science is traced in an effort to demonstrate the essential phenomenological aspects of the scientific methodology. Part II, on the other hand, is a technical exposition of some foundational aspects of quantum mechanics based on quantum logic. An effort is made to retain the theme that quantum mechanics is largely a phenomenological theory. As a summary, Part III constitutes an attempt to correlate the first two parts and to present tentatively some consequent reflections on the metaphysical significance of the quantum mechanical formalism.

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.

Anatolij Dvurečenskij