Center for Logic and the Philosophy of Science (CLWF, SWIJ)

and Center Leo Apostel (CLeA)

VUB, Brussels

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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