Abstract
Some critical open problems of epistemic logics can be investigated in the framework of a quantum computational approach. The basic idea is to interpret sentences like “Alice knows that Bob does not understand that π is irrational” as pieces of quantum information (generally represented by density operators of convenient Hilbert spaces). Logical epistemic operators (to understand, to know…) are dealt with as (generally irreversible) quantum operations, which are, in a sense, similar to measurement-procedures. This approach permits us to model some characteristic epistemic processes, that concern both human and artificial intelligence. For instance, the operation of “memorizing and retrieving information” can be formally represented, in this framework, by using a quantum teleportation phenomenon.
Similar content being viewed by others
Notes
References
Beltrametti, E., Dalla Chiara, M.L., Giuntini, R., Leporini, R., Sergioli, G.: Epistemic quantum computational structures in a Hilbert-space environment. Fundam. Inform. 115, 1–14 (2012). doi:10.3233/FI-2012-637
Beltrametti, E., Dalla Chiara, M.L., Giuntini, R., Sergioli, G.: Quantum teleportation and quantum epistemic semantics. Math. Slovaca 62, 1–24 (2012)
Chiribella, G., D’Ariano, G.M., Perinotti, P.: Transforming quantum operations: quantum supermaps. Europhys. Lett. 83, 1–6 (2008)
Dalla Chiara, M.L., Freytes, H., Giuntini, R., Ledda, A., Leporini, R., Sergioli, G.: Entanglement as a semantic resource. Found. Phys. 40, 1494–1518 (2011)
Fan, H.-y., Hu, L.-y.: Infinite-dimensional Kraus operators for describing amplitudue-damping channel and laser process. Opt. Commun. 282, 932–935 (2009)
Kraus, K.: States, Effects and Operations. Springer, Berlin (1983)
Leporini, R., Sergioli, G.: Quantum channels and knowledge operations (submitted)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Beltrametti, E., Dalla Chiara, M.L., Giuntini, R. et al. A Quantum Computational Semantics for Epistemic Logical Operators. Part I: Epistemic Structures. Int J Theor Phys 53, 3279–3292 (2014). https://doi.org/10.1007/s10773-013-1642-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-013-1642-z