LQP: The dynamic logic of quantum information

Mathematical Structures in Computer Science

Volumn 16, Issue 3, 2006, Pages 491-525

  Baltag, Alexandru ^a   Smets, Sonja ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750742754     PISSN: 09601295     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0960129506005299     Document Type: Conference Paper

References (39)

1. Abramsky, S. and Coecke, B. (2005) A Categorical Semantics of Quantum Protocols. To appear in the Proceedings of the 19th IEEE Conference on Logic in Computer Science (LiCS'04). (Also available as arXiv:quant-ph/0402130.)
2. Akatov, D. (2005) The Logic of Quantum Program Verification. Master's Thesis, Oxford University Computing Laboratory (to appear).
3. Amemiya, I. and Araki, H. (1967) A Remark on Piron's paper. Publications of the Research Institute of Mathematical Sciences Kyoto University, series A 2 423-427.
4. Amira, H., Coecke, B. and Stubbe, I. (1998) How Quantales Emerge by Introducing Induction within the Operational Approach. Helvetica Physica Acta 71 554-572.
5. Baltag, A. (2004) Dynamic and Epistemic Logics for Quantum Measurements. Presented at PML'04, Brussels 2004.
6. Baltag, A. and Smets, S. (2004) The Logic of Quantum Programs. In: Selinger, P. (ed.) Proceedings of QPL2004 (LICS'04 Workshop), TUCS General Publication 33, Turku Center for Computer Science 39-56.
7. Baltag, A. and Smets, S. (2005a) Complete Axiomatizations for Quantum Actions. Proceedings of IQSA'04. International Journal of Theoretical Physics (to appear).
8. Baltag, A. and Smets, S. (2005b) What can Logic learn from Quantum Mechanics? Presented at the Workshop on 'Quantum Information: Epistemological and Logic Lessons' of ECAP'05, Lisbon, Portugal.
9. Beltrametti, E.G. and Cassinelli, G. (1977) On State Transformations Induced by Yes-No Experiments, in the Context of Quantum Logic. Journal of Philosophical Logic 6 369-379
10. Brunet, O. and Jorrand, P. (2003) Dynamic Quantum Logic for Quantum Programs. Available as arXiv:quant-ph/0311143
11. Coecke, B. (2000) Structural Characterization of Compoundness. International Journal of Theoretical Physics 39 585-594.
12. Coecke, B. (2004) The Logic of Entanglement. arXiv: quant-ph/0402014.
13. Coecke, B., Moore, D. J. and Smets, S. (2004) Logic of Dynamics & Dynamics of Logic; Some Paradigm Examples. In: Rahman, S., Symons, J., Gabbay, D. M. and van Bendegem, J. P. (eds.) Logic, Epistemology and the Unity of Science.
14. Coecke, B., Moore, D. J. and Stubbe, I. (2001) Quantaloids describing Causation and Propagation for Physical Properties. Foundations of Physics Letters 14 357-367. (Also available as arXiv: quant-ph/0009100.)
15. Coecke, B. and Smets, S. (2004) The Sasaki Hook is not a [Static] Implicative Connective but Induces a Backward [in Time] Dynamic One that Assigns Causes. International Journal of Theoretical Physics 43(7-8) 1705-1736. (Also available as arXiv: quant-ph/0111076.)
16. Coecke, B. and Stubbe, I. (1999) On a Duality of Quantales Emerging from an Operational Resolution. International Journal of Theoretical Physics 38 3269-3281.
17. Dalla Chiara, M. L. and Giuntini, R. (2002) Quantum Logics. In: Gabbay, D. M. and Guenthner, F. (eds.) Handbook of Philosophical Logic 6, second edition, Kluwer 129-228.
18. Dalla Chiara, M. L., Guintini, R. and Greechie, R. (2004) Reasoning in Quantum Theory, Kluwer.
19. Daniel, W. (1982) On the Non-Unitary Evolution of Quantum Systems. Helvetica Physica Acta 55 330-338.
20. Daniel, W. (1989) Axiomatic Description of Irreversible and Reversible Evolution of a Physical System. Helvetica Physica Acta 62 941-968.
21. Faure, C. A., Moore, D. J. and Piron, C. (1995) Deterministic Evolutions and Schrodinger Flows. Helvetica Physica Acta 68 150-157.
22. Goldblatt, R. (1984) Orthomodularity is not elementary. The Journal of Symbolic Logic 49 401-404.
23. Goldblatt, R. (1974) Semantic Analysis of Orthologic. Journal of Philosophical Logic 3 19-35.
24. Gruska, J. (1999) Quantum Computing, McGraw-Hill, London.
25. Hardegree, G. M. (1975) Stalnaker Conditional and Quantum Logic. Journal of Philosophical Logic 4 399-421.
26. Hardegree, G. M. (1979) The Conditional in Abstract and Concrete Quantum Logic. In: Hooker, C. A. (ed.) The Logico-Algebraic Approach to Quantum Mechanics 2, Reidel.
27. Harel, D., Kozen, D. and Tiuryn, J. (2000) Dynamic Logic, MIT Press.
28. Jauch, J. M. (1968) Foundations of Quantum Mechanics, Addison-Wesley.
29. Jauch, J. M. and Piron, C. (1969) On the Structure of Quantal Proposition Systems. Helvetica Physica Acta 42 842-848.
30. Mateus, P. and Sernadas, A. (2004) Reasoning about Quantum Systems. In: Alferes, J. and Leite, J. (eds.) Springer-Verlag Lecture Notes in Artificial Intelligence 3229 239-251.
31. Mayet, R. (1998) Some Characterizations of the Underlying Division Ring of a Hilbert Lattice by Automorphisms. International Journal of Theoretical Physics 37 (1) 109-114.
32. Nielsen, M. and Chuang, I. L. (2000) Quantum Computation and Quantum Information, Cambridge University Press.
33. Piron, C. (1964) Axiomatique quantique (Ph.D. Thesis). Helvetica Physica Acta 37 439-468.
34. (English translation by Cole, M. Quantum Axiomatics, RB4 Technical memo 107/106/104, GPO Engineering Department, London).
35. Piron, C. (1976) Foundations of Quantum Physics, W. A. Benjamin.
36. Smets, S. (2001) On Causation and a Counterfactual in Quantum Logic: the Sasaki Hook. Logique et Analyse 173-175 307-325.
37. Smets, S. (2004) On Quantum Propositional Dynamic Logic. Presented at PML'04, Brussels 2004.
38. Smets, S. (2005) From Intuitionistic Logic to Dynamic Operational Quantum Logic. Poznan Studies in Philosophy and the Humanities (to appear).
39. Solèr, M. P. (1995) Characterization of Hilbert spaces by orthomodular spaces. Communications in Algebra 23 (1) 219-243.