Knowledge and common knowledge in a distributed environment
Journal of the ACM (JACM)
Reasoning about knowledge
Modal logic
A Categorical Semantics of Quantum Protocols
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
LQP: the dynamic logic of quantum information
Mathematical Structures in Computer Science
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In this paper we analyze classical and quantum correlations using the tools of epistemic logic. Our main contribution consists of two new logical systems. The first one is called General Epistemic Logic (GEL), it extends traditional epistemic logic with operators that allow us to reason about the information carried by a complex system composed of several parts. The second system is called the Logic of Correlated Knowledge (LCK), which extends GEL with sentences that describe the observational capabilities of an agent. On the semantic side we introduce correlation models, as a generalization of the ''interpreted systems'' semantics. We use this setting to investigate several types of informational correlations (e.g. distributed information, quantum correlated information) that complex systems can exhibit. We also provide an informational-logical characterization of the notion of ''quantum entanglement''.