Dynamic Quantum Logic

Sonja Smets
Center for Logic and the Philosophy of Science (CLWF, SWIJ)
and Center Leo Apostel (CLeA)
VUB, Brussels

Monday 20 September, 14 H
Séminaire 3, 3ème étage
Institut d'Informatique
rue Grandgagnage 21
5000 Namur

In this talk I will present the new results of my joint work with A. Baltag on Quantum Dynamic Logic, i.e. a logical calculus for "quantum information flow". Basically it comes down to a quantum version of PDL (Propositional Dynamic Logic), i.e. a logic equipped with dynamic modalities to deal with quantum measurements ("tests") and unitary evolutions. There will be two parts in this talk. In the first part I will start with a brief introduction to Standard Quantum Logic (SQL), focussing on "weak modularity" and the differences with classical Boolean logic. Next I will explain how a new "dynamic approach" transforms SQL into a nice and easy accessible structure. Indeed, SQL can be conceived as the negation-free "test only" fragment of Quantum Dynamic Logic. This involves a dynamic turn which yields new results and allows one to work with an unproblematic frame condition for weak modularity. On a conceptual level we see that quantum physics does not require a non-classical logic, but only a non-classical notion of physical (inter)action (in particular a non-classical notion of measurement). In the second part I will focus on the semantical structures associated with Quantum Dynamic Logic. In particular I will concentrate on Quantum Frames (i.e. a relational semantics) and briefly on Quantum Dynamic Algebras. I will mention the representation theorems (and corresponding completeness results) with respect to Hilbert spaces of dimension equal or greater than 4. And finally I will only briefly touch upon how one can extend this logic to deal with entanglement and compound quantum systems.
The slides in PostScript, LaTeX, DeVice-Independent, HyperText, Portable Document formats.
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