Both quantum logic (QL) and quantum information (QI) are based on viewing quantum mechanics in terms of concepts closely tied to information, so QL, should be closely connected to QI. On the whole, these two research fields are pursued by separate communities and so a closer collaboration is likely to yield significant insights into both. While taking a broad view of both fields, the workshop will focus on areas that we feel are most likely to spark significant collaboration and new research initiatives.
Languages (syntax of modal logic, dynamic logic, epistemic logic). Relational (Kripke) models. Algebraic models (quantales, dynamic algebras). Axioms.
Introductory lecture summary:
1. Finite dimensional hilbert spaces and (complemented) modular lattices; infinite-dimensional hilbert spaces and orthomodularity.
2. von Neumann's QL; von Neumann-Birkhoff (briefly!); reconstruction of QM from P(H)
3. Mackey's programme; some early axiomatics (e.g., Zierler); QLs as OMPs + order-determining sets of states
4. Piron's Theorem; some discussion of Piron's axioms
5. Keller's examples (maybe just a mention, though I'd like to indicate how they come up); Soler's theorem (just the statement)